1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /*************************************************************** |
---|
5 | * File: sca.cc |
---|
6 | * Purpose: supercommutative kernel procedures |
---|
7 | * Author: motsak (Oleksandr Motsak) |
---|
8 | * Created: 2006/12/18 |
---|
9 | * Version: $Id$ |
---|
10 | *******************************************************************/ |
---|
11 | |
---|
12 | // set it here if needed. |
---|
13 | #define OUTPUT 0 |
---|
14 | #define MYTEST 0 |
---|
15 | |
---|
16 | #if MYTEST |
---|
17 | #define OM_CHECK 4 |
---|
18 | #define OM_TRACK 5 |
---|
19 | #endif |
---|
20 | |
---|
21 | // #define PDEBUG 2 |
---|
22 | #include "config.h" |
---|
23 | #include <misc/auxiliary.h> |
---|
24 | |
---|
25 | #ifdef HAVE_PLURAL |
---|
26 | |
---|
27 | // for |
---|
28 | #define PLURAL_INTERNAL_DECLARATIONS |
---|
29 | #include <polys/nc/sca.h> |
---|
30 | #include <polys/nc/nc.h> |
---|
31 | // #include <polys/gring.h> |
---|
32 | |
---|
33 | |
---|
34 | #include <coeffs/numbers.h> |
---|
35 | #include <polys/coeffrings.h> |
---|
36 | |
---|
37 | |
---|
38 | // #include <polys/febase.h> |
---|
39 | #include <misc/options.h> |
---|
40 | |
---|
41 | #include <polys/monomials/p_polys.h> |
---|
42 | |
---|
43 | // #include <polys/kutil.h> |
---|
44 | #include <polys/simpleideals.h> |
---|
45 | #include <misc/intvec.h> |
---|
46 | // #include <polys/polys.h> |
---|
47 | |
---|
48 | #include <polys/monomials/ring.h> |
---|
49 | #include <polys/matpol.h> |
---|
50 | #include <polys/kbuckets.h> |
---|
51 | // #include <polys/kstd1.h> |
---|
52 | #include <polys/sbuckets.h> |
---|
53 | |
---|
54 | #include <polys/prCopy.h> |
---|
55 | |
---|
56 | #include <polys/operations/p_Mult_q.h> |
---|
57 | #include <polys/templates/p_MemAdd.h> |
---|
58 | |
---|
59 | // #include <polys/kutil.h> |
---|
60 | // #include <polys/kstd1.h> |
---|
61 | |
---|
62 | #include <polys/weight.h> |
---|
63 | |
---|
64 | |
---|
65 | // poly functions defined in p_Procs : |
---|
66 | |
---|
67 | // return pPoly * pMonom; preserve pPoly and pMonom. |
---|
68 | poly sca_pp_Mult_mm(const poly pPoly, const poly pMonom, const ring rRing, poly &); |
---|
69 | |
---|
70 | // return pMonom * pPoly; preserve pPoly and pMonom. |
---|
71 | static poly sca_mm_Mult_pp(const poly pMonom, const poly pPoly, const ring rRing); |
---|
72 | |
---|
73 | // return pPoly * pMonom; preserve pMonom, destroy or reuse pPoly. |
---|
74 | poly sca_p_Mult_mm(poly pPoly, const poly pMonom, const ring rRing); |
---|
75 | |
---|
76 | // return pMonom * pPoly; preserve pMonom, destroy or reuse pPoly. |
---|
77 | static poly sca_mm_Mult_p(const poly pMonom, poly pPoly, const ring rRing); |
---|
78 | |
---|
79 | |
---|
80 | // compute the spolynomial of p1 and p2 |
---|
81 | poly sca_SPoly(const poly p1, const poly p2, const ring r); |
---|
82 | poly sca_ReduceSpoly(const poly p1, poly p2, const ring r); |
---|
83 | |
---|
84 | // Modified Plural's Buchberger's algorithmus. |
---|
85 | ideal sca_gr_bba(const ideal F, const ideal Q, const intvec *, const intvec *, kStrategy strat, const ring _currRing); |
---|
86 | |
---|
87 | // Modified modern Sinuglar Buchberger's algorithm. |
---|
88 | ideal sca_bba(const ideal F, const ideal Q, const intvec *w, const intvec *, kStrategy strat, const ring _currRing); |
---|
89 | |
---|
90 | // Modified modern Sinuglar Mora's algorithm. |
---|
91 | ideal sca_mora(const ideal F, const ideal Q, const intvec *w, const intvec *, kStrategy strat, const ring _currRing); |
---|
92 | |
---|
93 | |
---|
94 | |
---|
95 | //////////////////////////////////////////////////////////////////////////////////////////////////// |
---|
96 | // Super Commutative Algebra extension by Oleksandr |
---|
97 | //////////////////////////////////////////////////////////////////////////////////////////////////// |
---|
98 | |
---|
99 | /* |
---|
100 | static inline ring assureCurrentRing(ring r) |
---|
101 | { |
---|
102 | ring save = currRing; |
---|
103 | |
---|
104 | if( currRing != r ) |
---|
105 | rChangeCurrRing(r); |
---|
106 | |
---|
107 | return save; |
---|
108 | } |
---|
109 | */ |
---|
110 | |
---|
111 | |
---|
112 | |
---|
113 | // returns the sign of: lm(pMonomM) * lm(pMonomMM), |
---|
114 | // preserves input, may return +/-1, 0 |
---|
115 | static inline int sca_Sign_mm_Mult_mm( const poly pMonomM, const poly pMonomMM, const ring rRing ) |
---|
116 | { |
---|
117 | #ifdef PDEBUG |
---|
118 | p_Test(pMonomM, rRing); |
---|
119 | p_Test(pMonomMM, rRing); |
---|
120 | #endif |
---|
121 | |
---|
122 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
---|
123 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
---|
124 | |
---|
125 | register unsigned int tpower = 0; |
---|
126 | register unsigned int cpower = 0; |
---|
127 | |
---|
128 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
---|
129 | { |
---|
130 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
---|
131 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
---|
132 | |
---|
133 | #ifdef PDEBUG |
---|
134 | assume( iExpM <= 1); |
---|
135 | assume( iExpMM <= 1); |
---|
136 | #endif |
---|
137 | |
---|
138 | if( iExpMM != 0 ) // TODO: think about eliminating there if-s... |
---|
139 | { |
---|
140 | if( iExpM != 0 ) |
---|
141 | { |
---|
142 | return 0; // lm(pMonomM) * lm(pMonomMM) == 0 |
---|
143 | } |
---|
144 | tpower ^= cpower; // compute degree of (-1). |
---|
145 | } |
---|
146 | cpower ^= iExpM; |
---|
147 | } |
---|
148 | |
---|
149 | #ifdef PDEBUG |
---|
150 | assume(tpower <= 1); |
---|
151 | #endif |
---|
152 | |
---|
153 | // 1 => -1 // degree is odd => negate coeff. |
---|
154 | // 0 => 1 |
---|
155 | |
---|
156 | return(1 - (tpower << 1) ); |
---|
157 | } |
---|
158 | |
---|
159 | |
---|
160 | |
---|
161 | |
---|
162 | // returns and changes pMonomM: lt(pMonomM) = lt(pMonomM) * lt(pMonomMM), |
---|
163 | // preserves pMonomMM. may return NULL! |
---|
164 | // if result != NULL => next(result) = next(pMonomM), lt(result) = lt(pMonomM) * lt(pMonomMM) |
---|
165 | // if result == NULL => pMonomM MUST BE deleted manually! |
---|
166 | static inline poly sca_m_Mult_mm( poly pMonomM, const poly pMonomMM, const ring rRing ) |
---|
167 | { |
---|
168 | #ifdef PDEBUG |
---|
169 | p_Test(pMonomM, rRing); |
---|
170 | p_Test(pMonomMM, rRing); |
---|
171 | #endif |
---|
172 | |
---|
173 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
---|
174 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
---|
175 | |
---|
176 | register unsigned int tpower = 0; |
---|
177 | register unsigned int cpower = 0; |
---|
178 | |
---|
179 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
---|
180 | { |
---|
181 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
---|
182 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
---|
183 | |
---|
184 | #ifdef PDEBUG |
---|
185 | assume( iExpM <= 1); |
---|
186 | assume( iExpMM <= 1); |
---|
187 | #endif |
---|
188 | |
---|
189 | if( iExpMM != 0 ) |
---|
190 | { |
---|
191 | if( iExpM != 0 ) // result is zero! |
---|
192 | { |
---|
193 | return NULL; // we do nothing with pMonomM in this case! |
---|
194 | } |
---|
195 | |
---|
196 | tpower ^= cpower; // compute degree of (-1). |
---|
197 | } |
---|
198 | |
---|
199 | cpower ^= iExpM; |
---|
200 | } |
---|
201 | |
---|
202 | #ifdef PDEBUG |
---|
203 | assume(tpower <= 1); |
---|
204 | #endif |
---|
205 | |
---|
206 | p_ExpVectorAdd(pMonomM, pMonomMM, rRing); // "exponents" are additive!!! |
---|
207 | |
---|
208 | number nCoeffM = p_GetCoeff(pMonomM, rRing); // no new copy! should be deleted! |
---|
209 | |
---|
210 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
---|
211 | nCoeffM = n_Neg(nCoeffM, rRing); // negate nCoeff (will destroy the original number) |
---|
212 | |
---|
213 | const number nCoeffMM = p_GetCoeff(pMonomMM, rRing); // no new copy! |
---|
214 | |
---|
215 | number nCoeff = n_Mult(nCoeffM, nCoeffMM, rRing); // new number! |
---|
216 | |
---|
217 | p_SetCoeff(pMonomM, nCoeff, rRing); // delete lc(pMonomM) and set lc(pMonomM) = nCoeff |
---|
218 | |
---|
219 | #ifdef PDEBUG |
---|
220 | p_LmTest(pMonomM, rRing); |
---|
221 | #endif |
---|
222 | |
---|
223 | return(pMonomM); |
---|
224 | } |
---|
225 | |
---|
226 | // returns and changes pMonomM: lt(pMonomM) = lt(pMonomMM) * lt(pMonomM), |
---|
227 | // preserves pMonomMM. may return NULL! |
---|
228 | // if result != NULL => next(result) = next(pMonomM), lt(result) = lt(pMonomMM) * lt(pMonomM) |
---|
229 | // if result == NULL => pMonomM MUST BE deleted manually! |
---|
230 | static inline poly sca_mm_Mult_m( const poly pMonomMM, poly pMonomM, const ring rRing ) |
---|
231 | { |
---|
232 | #ifdef PDEBUG |
---|
233 | p_Test(pMonomM, rRing); |
---|
234 | p_Test(pMonomMM, rRing); |
---|
235 | #endif |
---|
236 | |
---|
237 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
---|
238 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
---|
239 | |
---|
240 | register unsigned int tpower = 0; |
---|
241 | register unsigned int cpower = 0; |
---|
242 | |
---|
243 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
---|
244 | { |
---|
245 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
---|
246 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
---|
247 | |
---|
248 | #ifdef PDEBUG |
---|
249 | assume( iExpM <= 1); |
---|
250 | assume( iExpMM <= 1); |
---|
251 | #endif |
---|
252 | |
---|
253 | if( iExpM != 0 ) |
---|
254 | { |
---|
255 | if( iExpMM != 0 ) // result is zero! |
---|
256 | { |
---|
257 | return NULL; // we do nothing with pMonomM in this case! |
---|
258 | } |
---|
259 | |
---|
260 | tpower ^= cpower; // compute degree of (-1). |
---|
261 | } |
---|
262 | |
---|
263 | cpower ^= iExpMM; |
---|
264 | } |
---|
265 | |
---|
266 | #ifdef PDEBUG |
---|
267 | assume(tpower <= 1); |
---|
268 | #endif |
---|
269 | |
---|
270 | p_ExpVectorAdd(pMonomM, pMonomMM, rRing); // "exponents" are additive!!! |
---|
271 | |
---|
272 | number nCoeffM = p_GetCoeff(pMonomM, rRing); // no new copy! should be deleted! |
---|
273 | |
---|
274 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
---|
275 | nCoeffM = n_Neg(nCoeffM, rRing); // negate nCoeff (will destroy the original number), creates new number! |
---|
276 | |
---|
277 | const number nCoeffMM = p_GetCoeff(pMonomMM, rRing); // no new copy! |
---|
278 | |
---|
279 | number nCoeff = n_Mult(nCoeffM, nCoeffMM, rRing); // new number! |
---|
280 | |
---|
281 | p_SetCoeff(pMonomM, nCoeff, rRing); // delete lc(pMonomM) and set lc(pMonomM) = nCoeff |
---|
282 | |
---|
283 | #ifdef PDEBUG |
---|
284 | p_LmTest(pMonomM, rRing); |
---|
285 | #endif |
---|
286 | |
---|
287 | return(pMonomM); |
---|
288 | } |
---|
289 | |
---|
290 | |
---|
291 | |
---|
292 | // returns: result = lt(pMonom1) * lt(pMonom2), |
---|
293 | // preserves pMonom1, pMonom2. may return NULL! |
---|
294 | // if result != NULL => next(result) = NULL, lt(result) = lt(pMonom1) * lt(pMonom2) |
---|
295 | static inline poly sca_mm_Mult_mm( poly pMonom1, const poly pMonom2, const ring rRing ) |
---|
296 | { |
---|
297 | #ifdef PDEBUG |
---|
298 | p_Test(pMonom1, rRing); |
---|
299 | p_Test(pMonom2, rRing); |
---|
300 | #endif |
---|
301 | |
---|
302 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
---|
303 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
---|
304 | |
---|
305 | register unsigned int tpower = 0; |
---|
306 | register unsigned int cpower = 0; |
---|
307 | |
---|
308 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
---|
309 | { |
---|
310 | const unsigned int iExp1 = p_GetExp(pMonom1, j, rRing); |
---|
311 | const unsigned int iExp2 = p_GetExp(pMonom2, j, rRing); |
---|
312 | |
---|
313 | #ifdef PDEBUG |
---|
314 | assume( iExp1 <= 1); |
---|
315 | assume( iExp2 <= 1); |
---|
316 | #endif |
---|
317 | |
---|
318 | if( iExp2 != 0 ) |
---|
319 | { |
---|
320 | if( iExp1 != 0 ) // result is zero! |
---|
321 | { |
---|
322 | return NULL; |
---|
323 | } |
---|
324 | tpower ^= cpower; // compute degree of (-1). |
---|
325 | } |
---|
326 | cpower ^= iExp1; |
---|
327 | } |
---|
328 | |
---|
329 | #ifdef PDEBUG |
---|
330 | assume(cpower <= 1); |
---|
331 | #endif |
---|
332 | |
---|
333 | poly pResult; |
---|
334 | p_AllocBin(pResult,rRing->PolyBin,rRing); |
---|
335 | |
---|
336 | p_ExpVectorSum(pResult, pMonom1, pMonom2, rRing); // "exponents" are additive!!! |
---|
337 | |
---|
338 | pNext(pResult) = NULL; |
---|
339 | |
---|
340 | const number nCoeff1 = p_GetCoeff(pMonom1, rRing); // no new copy! |
---|
341 | const number nCoeff2 = p_GetCoeff(pMonom2, rRing); // no new copy! |
---|
342 | |
---|
343 | number nCoeff = n_Mult(nCoeff1, nCoeff2, rRing); // new number! |
---|
344 | |
---|
345 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
---|
346 | nCoeff = n_Neg(nCoeff, rRing); // negate nCoeff (will destroy the original number) |
---|
347 | |
---|
348 | p_SetCoeff0(pResult, nCoeff, rRing); // set lc(pResult) = nCoeff, no destruction! |
---|
349 | |
---|
350 | #ifdef PDEBUG |
---|
351 | p_LmTest(pResult, rRing); |
---|
352 | #endif |
---|
353 | |
---|
354 | return(pResult); |
---|
355 | } |
---|
356 | |
---|
357 | // returns: result = x_i * lt(pMonom), |
---|
358 | // preserves pMonom. may return NULL! |
---|
359 | // if result != NULL => next(result) = NULL, lt(result) = x_i * lt(pMonom) |
---|
360 | static inline poly sca_xi_Mult_mm(unsigned int i, const poly pMonom, const ring rRing) |
---|
361 | { |
---|
362 | #ifdef PDEBUG |
---|
363 | p_Test(pMonom, rRing); |
---|
364 | #endif |
---|
365 | |
---|
366 | assume( i <= scaLastAltVar(rRing)); |
---|
367 | assume( scaFirstAltVar(rRing) <= i ); |
---|
368 | |
---|
369 | if( p_GetExp(pMonom, i, rRing) != 0 ) // => result is zero! |
---|
370 | return NULL; |
---|
371 | |
---|
372 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
---|
373 | |
---|
374 | register unsigned int cpower = 0; |
---|
375 | |
---|
376 | for( register unsigned int j = iFirstAltVar; j < i ; j++ ) |
---|
377 | cpower ^= p_GetExp(pMonom, j, rRing); |
---|
378 | |
---|
379 | #ifdef PDEBUG |
---|
380 | assume(cpower <= 1); |
---|
381 | #endif |
---|
382 | |
---|
383 | poly pResult = p_LmInit(pMonom, rRing); |
---|
384 | |
---|
385 | p_SetExp(pResult, i, 1, rRing); // pResult*=X_i && |
---|
386 | p_Setm(pResult, rRing); // addjust degree after previous step! |
---|
387 | |
---|
388 | number nCoeff = n_Copy(p_GetCoeff(pMonom, rRing), rRing); // new number! |
---|
389 | |
---|
390 | if( cpower != 0 ) // degree is odd => negate coeff. |
---|
391 | nCoeff = n_Neg(nCoeff, rRing); // negate nCoeff (will destroy the original number) |
---|
392 | |
---|
393 | p_SetCoeff0(pResult, nCoeff, rRing); // set lc(pResult) = nCoeff, no destruction! |
---|
394 | |
---|
395 | #ifdef PDEBUG |
---|
396 | p_LmTest(pResult, rRing); |
---|
397 | #endif |
---|
398 | |
---|
399 | return(pResult); |
---|
400 | } |
---|
401 | |
---|
402 | //-----------------------------------------------------------------------------------// |
---|
403 | |
---|
404 | // return poly = pPoly * pMonom; preserve pMonom, destroy or reuse pPoly. |
---|
405 | poly sca_p_Mult_mm(poly pPoly, const poly pMonom, const ring rRing) |
---|
406 | { |
---|
407 | assume( rIsSCA(rRing) ); |
---|
408 | |
---|
409 | #ifdef PDEBUG |
---|
410 | // Print("sca_p_Mult_mm\n"); // ! |
---|
411 | |
---|
412 | p_Test(pPoly, rRing); |
---|
413 | p_Test(pMonom, rRing); |
---|
414 | #endif |
---|
415 | |
---|
416 | if( pPoly == NULL ) |
---|
417 | return NULL; |
---|
418 | |
---|
419 | assume(pMonom !=NULL); |
---|
420 | //if( pMonom == NULL ) |
---|
421 | //{ |
---|
422 | // // pPoly != NULL => |
---|
423 | // p_Delete( &pPoly, rRing ); |
---|
424 | // return NULL; |
---|
425 | //} |
---|
426 | |
---|
427 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
428 | |
---|
429 | poly p = pPoly; poly* ppPrev = &pPoly; |
---|
430 | |
---|
431 | loop |
---|
432 | { |
---|
433 | #ifdef PDEBUG |
---|
434 | p_Test(p, rRing); |
---|
435 | #endif |
---|
436 | const int iComponent = p_GetComp(p, rRing); |
---|
437 | |
---|
438 | if( iComponent!=0 ) |
---|
439 | { |
---|
440 | if( iComponentMonomM!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
---|
441 | { |
---|
442 | // REPORT_ERROR |
---|
443 | Werror("sca_p_Mult_mm: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
444 | // what should we do further?!? |
---|
445 | |
---|
446 | p_Delete( &pPoly, rRing); // delete the result AND rest |
---|
447 | return NULL; |
---|
448 | } |
---|
449 | #ifdef PDEBUG |
---|
450 | if(iComponentMonomM==0 ) |
---|
451 | { |
---|
452 | dReportError("sca_p_Mult_mm: Multiplication in the left module from the right"); |
---|
453 | } |
---|
454 | #endif |
---|
455 | } |
---|
456 | |
---|
457 | // terms will be in the same order because of quasi-ordering! |
---|
458 | poly v = sca_m_Mult_mm(p, pMonom, rRing); |
---|
459 | |
---|
460 | if( v != NULL ) |
---|
461 | { |
---|
462 | ppPrev = &pNext(p); // fixed! |
---|
463 | |
---|
464 | // *p is changed if v != NULL ( p == v ) |
---|
465 | pIter(p); |
---|
466 | |
---|
467 | if( p == NULL ) |
---|
468 | break; |
---|
469 | } |
---|
470 | else |
---|
471 | { // Upps! Zero!!! we must kill this term! |
---|
472 | |
---|
473 | // |
---|
474 | p = p_LmDeleteAndNext(p, rRing); |
---|
475 | |
---|
476 | *ppPrev = p; |
---|
477 | |
---|
478 | if( p == NULL ) |
---|
479 | break; |
---|
480 | } |
---|
481 | } |
---|
482 | |
---|
483 | #ifdef PDEBUG |
---|
484 | p_Test(pPoly,rRing); |
---|
485 | #endif |
---|
486 | |
---|
487 | return(pPoly); |
---|
488 | } |
---|
489 | |
---|
490 | // return new poly = pPoly * pMonom; preserve pPoly and pMonom. |
---|
491 | poly sca_pp_Mult_mm(const poly pPoly, const poly pMonom, const ring rRing, poly &) |
---|
492 | { |
---|
493 | assume( rIsSCA(rRing) ); |
---|
494 | |
---|
495 | #ifdef PDEBUG |
---|
496 | // Print("sca_pp_Mult_mm\n"); // ! |
---|
497 | |
---|
498 | p_Test(pPoly, rRing); |
---|
499 | p_Test(pMonom, rRing); |
---|
500 | #endif |
---|
501 | |
---|
502 | if( ( pPoly == NULL ) /*|| ( pMonom == NULL )*/ ) |
---|
503 | return NULL; |
---|
504 | |
---|
505 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
506 | |
---|
507 | poly pResult = NULL; |
---|
508 | poly* ppPrev = &pResult; |
---|
509 | |
---|
510 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
---|
511 | { |
---|
512 | #ifdef PDEBUG |
---|
513 | p_Test(p, rRing); |
---|
514 | #endif |
---|
515 | const int iComponent = p_GetComp(p, rRing); |
---|
516 | |
---|
517 | if( iComponent!=0 ) |
---|
518 | { |
---|
519 | if( iComponentMonomM!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
---|
520 | { |
---|
521 | // REPORT_ERROR |
---|
522 | Werror("sca_pp_Mult_mm: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
523 | // what should we do further?!? |
---|
524 | |
---|
525 | p_Delete( &pResult, rRing); // delete the result |
---|
526 | return NULL; |
---|
527 | } |
---|
528 | |
---|
529 | #ifdef PDEBUG |
---|
530 | if(iComponentMonomM==0 ) |
---|
531 | { |
---|
532 | dReportError("sca_pp_Mult_mm: Multiplication in the left module from the right"); |
---|
533 | } |
---|
534 | #endif |
---|
535 | } |
---|
536 | |
---|
537 | // terms will be in the same order because of quasi-ordering! |
---|
538 | poly v = sca_mm_Mult_mm(p, pMonom, rRing); |
---|
539 | |
---|
540 | if( v != NULL ) |
---|
541 | { |
---|
542 | *ppPrev = v; |
---|
543 | ppPrev = &pNext(v); |
---|
544 | } |
---|
545 | } |
---|
546 | |
---|
547 | #ifdef PDEBUG |
---|
548 | p_Test(pResult,rRing); |
---|
549 | #endif |
---|
550 | |
---|
551 | return(pResult); |
---|
552 | } |
---|
553 | |
---|
554 | //-----------------------------------------------------------------------------------// |
---|
555 | |
---|
556 | // return x_i * pPoly; preserve pPoly. |
---|
557 | static inline poly sca_xi_Mult_pp(unsigned int i, const poly pPoly, const ring rRing) |
---|
558 | { |
---|
559 | assume( rIsSCA(rRing) ); |
---|
560 | |
---|
561 | #ifdef PDEBUG |
---|
562 | p_Test(pPoly, rRing); |
---|
563 | #endif |
---|
564 | |
---|
565 | assume(i <= scaLastAltVar(rRing)); |
---|
566 | assume(scaFirstAltVar(rRing) <= i); |
---|
567 | |
---|
568 | if( pPoly == NULL ) |
---|
569 | return NULL; |
---|
570 | |
---|
571 | poly pResult = NULL; |
---|
572 | poly* ppPrev = &pResult; |
---|
573 | |
---|
574 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
---|
575 | { |
---|
576 | |
---|
577 | // terms will be in the same order because of quasi-ordering! |
---|
578 | poly v = sca_xi_Mult_mm(i, p, rRing); |
---|
579 | |
---|
580 | #ifdef PDEBUG |
---|
581 | p_Test(v, rRing); |
---|
582 | #endif |
---|
583 | |
---|
584 | if( v != NULL ) |
---|
585 | { |
---|
586 | *ppPrev = v; |
---|
587 | ppPrev = &pNext(*ppPrev); |
---|
588 | } |
---|
589 | } |
---|
590 | |
---|
591 | |
---|
592 | #ifdef PDEBUG |
---|
593 | p_Test(pResult, rRing); |
---|
594 | #endif |
---|
595 | |
---|
596 | return(pResult); |
---|
597 | } |
---|
598 | |
---|
599 | |
---|
600 | // return new poly = pMonom * pPoly; preserve pPoly and pMonom. |
---|
601 | static poly sca_mm_Mult_pp(const poly pMonom, const poly pPoly, const ring rRing) |
---|
602 | { |
---|
603 | assume( rIsSCA(rRing) ); |
---|
604 | |
---|
605 | #ifdef PDEBUG |
---|
606 | // Print("sca_mm_Mult_pp\n"); // ! |
---|
607 | |
---|
608 | p_Test(pPoly, rRing); |
---|
609 | p_Test(pMonom, rRing); |
---|
610 | #endif |
---|
611 | |
---|
612 | if ((pPoly==NULL) || (pMonom==NULL)) return NULL; |
---|
613 | |
---|
614 | assume( (pPoly != NULL) && (pMonom !=NULL)); |
---|
615 | |
---|
616 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
617 | |
---|
618 | poly pResult = NULL; |
---|
619 | poly* ppPrev = &pResult; |
---|
620 | |
---|
621 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
---|
622 | { |
---|
623 | #ifdef PDEBUG |
---|
624 | p_Test(p, rRing); |
---|
625 | #endif |
---|
626 | const int iComponent = p_GetComp(p, rRing); |
---|
627 | |
---|
628 | if( iComponentMonomM!=0 ) |
---|
629 | { |
---|
630 | if( iComponent!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
---|
631 | { |
---|
632 | // REPORT_ERROR |
---|
633 | Werror("sca_mm_Mult_pp: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
634 | // what should we do further?!? |
---|
635 | |
---|
636 | p_Delete( &pResult, rRing); // delete the result |
---|
637 | return NULL; |
---|
638 | } |
---|
639 | #ifdef PDEBUG |
---|
640 | if(iComponent==0 ) |
---|
641 | { |
---|
642 | dReportError("sca_mm_Mult_pp: Multiplication in the left module from the right!"); |
---|
643 | // PrintS("mm = "); p_Write(pMonom, rRing); |
---|
644 | // PrintS("pp = "); p_Write(pPoly, rRing); |
---|
645 | // assume(iComponent!=0); |
---|
646 | } |
---|
647 | #endif |
---|
648 | } |
---|
649 | |
---|
650 | // terms will be in the same order because of quasi-ordering! |
---|
651 | poly v = sca_mm_Mult_mm(pMonom, p, rRing); |
---|
652 | |
---|
653 | if( v != NULL ) |
---|
654 | { |
---|
655 | *ppPrev = v; |
---|
656 | ppPrev = &pNext(*ppPrev); // nice line ;-) |
---|
657 | } |
---|
658 | } |
---|
659 | |
---|
660 | #ifdef PDEBUG |
---|
661 | p_Test(pResult,rRing); |
---|
662 | #endif |
---|
663 | |
---|
664 | return(pResult); |
---|
665 | } |
---|
666 | |
---|
667 | |
---|
668 | // return poly = pMonom * pPoly; preserve pMonom, destroy or reuse pPoly. |
---|
669 | static poly sca_mm_Mult_p(const poly pMonom, poly pPoly, const ring rRing) // !!!!! the MOST used procedure !!!!! |
---|
670 | { |
---|
671 | assume( rIsSCA(rRing) ); |
---|
672 | |
---|
673 | #ifdef PDEBUG |
---|
674 | p_Test(pPoly, rRing); |
---|
675 | p_Test(pMonom, rRing); |
---|
676 | #endif |
---|
677 | |
---|
678 | if( pPoly == NULL ) |
---|
679 | return NULL; |
---|
680 | |
---|
681 | assume(pMonom!=NULL); |
---|
682 | //if( pMonom == NULL ) |
---|
683 | //{ |
---|
684 | // // pPoly != NULL => |
---|
685 | // p_Delete( &pPoly, rRing ); |
---|
686 | // return NULL; |
---|
687 | //} |
---|
688 | |
---|
689 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
690 | |
---|
691 | poly p = pPoly; poly* ppPrev = &pPoly; |
---|
692 | |
---|
693 | loop |
---|
694 | { |
---|
695 | #ifdef PDEBUG |
---|
696 | if( !p_Test(p, rRing) ) |
---|
697 | { |
---|
698 | PrintS("p is wrong!"); |
---|
699 | p_Write(p,rRing); |
---|
700 | } |
---|
701 | #endif |
---|
702 | |
---|
703 | const int iComponent = p_GetComp(p, rRing); |
---|
704 | |
---|
705 | if( iComponentMonomM!=0 ) |
---|
706 | { |
---|
707 | if( iComponent!=0 ) |
---|
708 | { |
---|
709 | // REPORT_ERROR |
---|
710 | Werror("sca_mm_Mult_p: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
711 | // what should we do further?!? |
---|
712 | |
---|
713 | p_Delete( &pPoly, rRing); // delete the result |
---|
714 | return NULL; |
---|
715 | } |
---|
716 | #ifdef PDEBUG |
---|
717 | if(iComponent==0) |
---|
718 | { |
---|
719 | dReportError("sca_mm_Mult_p: Multiplication in the left module from the right!"); |
---|
720 | // PrintS("mm = "); p_Write(pMonom, rRing); |
---|
721 | // PrintS("p = "); p_Write(pPoly, rRing); |
---|
722 | // assume(iComponent!=0); |
---|
723 | } |
---|
724 | #endif |
---|
725 | } |
---|
726 | |
---|
727 | // terms will be in the same order because of quasi-ordering! |
---|
728 | poly v = sca_mm_Mult_m(pMonom, p, rRing); |
---|
729 | |
---|
730 | if( v != NULL ) |
---|
731 | { |
---|
732 | ppPrev = &pNext(p); |
---|
733 | |
---|
734 | // *p is changed if v != NULL ( p == v ) |
---|
735 | pIter(p); |
---|
736 | |
---|
737 | if( p == NULL ) |
---|
738 | break; |
---|
739 | } |
---|
740 | else |
---|
741 | { // Upps! Zero!!! we must kill this term! |
---|
742 | p = p_LmDeleteAndNext(p, rRing); |
---|
743 | |
---|
744 | *ppPrev = p; |
---|
745 | |
---|
746 | if( p == NULL ) |
---|
747 | break; |
---|
748 | } |
---|
749 | } |
---|
750 | |
---|
751 | #ifdef PDEBUG |
---|
752 | if( !p_Test(pPoly, rRing) ) |
---|
753 | { |
---|
754 | PrintS("pPoly is wrong!"); |
---|
755 | p_Write(pPoly, rRing); |
---|
756 | } |
---|
757 | #endif |
---|
758 | |
---|
759 | return(pPoly); |
---|
760 | } |
---|
761 | |
---|
762 | //-----------------------------------------------------------------------------------// |
---|
763 | |
---|
764 | #ifdef PDEBUG |
---|
765 | #endif |
---|
766 | |
---|
767 | |
---|
768 | |
---|
769 | |
---|
770 | //-----------------------------------------------------------------------------------// |
---|
771 | |
---|
772 | // GB computation routines: |
---|
773 | |
---|
774 | /*4 |
---|
775 | * creates the S-polynomial of p1 and p2 |
---|
776 | * does not destroy p1 and p2 |
---|
777 | */ |
---|
778 | poly sca_SPoly( const poly p1, const poly p2, const ring r ) |
---|
779 | { |
---|
780 | assume( rIsSCA(r) ); |
---|
781 | |
---|
782 | const long lCompP1 = p_GetComp(p1,r); |
---|
783 | const long lCompP2 = p_GetComp(p2,r); |
---|
784 | |
---|
785 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
786 | { |
---|
787 | #ifdef PDEBUG |
---|
788 | dReportError("sca_SPoly: different non-zero components!\n"); |
---|
789 | #endif |
---|
790 | return(NULL); |
---|
791 | } |
---|
792 | |
---|
793 | poly pL = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r); // pL = lcm( lm(p1), lm(p2) ) |
---|
794 | |
---|
795 | poly m1 = p_One( r); |
---|
796 | p_ExpVectorDiff(m1, pL, p1, r); // m1 = pL / lm(p1) |
---|
797 | |
---|
798 | //p_SetComp(m1,0,r); |
---|
799 | //p_Setm(m1,r); |
---|
800 | #ifdef PDEBUG |
---|
801 | p_Test(m1,r); |
---|
802 | #endif |
---|
803 | |
---|
804 | |
---|
805 | poly m2 = p_One( r); |
---|
806 | p_ExpVectorDiff (m2, pL, p2, r); // m2 = pL / lm(p2) |
---|
807 | |
---|
808 | //p_SetComp(m2,0,r); |
---|
809 | //p_Setm(m2,r); |
---|
810 | #ifdef PDEBUG |
---|
811 | p_Test(m2,r); |
---|
812 | #endif |
---|
813 | |
---|
814 | p_Delete(&pL,r); |
---|
815 | |
---|
816 | number C1 = n_Copy(p_GetCoeff(p1,r),r); // C1 = lc(p1) |
---|
817 | number C2 = n_Copy(p_GetCoeff(p2,r),r); // C2 = lc(p2) |
---|
818 | |
---|
819 | number C = n_Gcd(C1,C2,r); // C = gcd(C1, C2) |
---|
820 | |
---|
821 | if (!n_IsOne(C, r)) // if C != 1 |
---|
822 | { |
---|
823 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
824 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
825 | } |
---|
826 | |
---|
827 | n_Delete(&C,r); // destroy the number C |
---|
828 | |
---|
829 | const int iSignSum = sca_Sign_mm_Mult_mm (m1, p1, r) + sca_Sign_mm_Mult_mm (m2, p2, r); |
---|
830 | // zero if different signs |
---|
831 | |
---|
832 | assume( (iSignSum*iSignSum == 0) || (iSignSum*iSignSum == 4) ); |
---|
833 | |
---|
834 | if( iSignSum != 0 ) // the same sign! |
---|
835 | C2=n_Neg (C2, r); |
---|
836 | |
---|
837 | p_SetCoeff(m1, C2, r); // lc(m1) = C2!!! |
---|
838 | p_SetCoeff(m2, C1, r); // lc(m2) = C1!!! |
---|
839 | |
---|
840 | poly tmp1 = nc_mm_Mult_pp (m1, pNext(p1), r); // tmp1 = m1 * tail(p1), |
---|
841 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
842 | |
---|
843 | poly tmp2 = nc_mm_Mult_pp (m2, pNext(p2), r); // tmp1 = m2 * tail(p2), |
---|
844 | p_Delete(&m2,r); // => n_Delete(&C1,r); |
---|
845 | |
---|
846 | poly spoly = p_Add_q (tmp1, tmp2, r); // spoly = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete tmp1,2 |
---|
847 | |
---|
848 | if (spoly!=NULL) p_Cleardenom (spoly, r); |
---|
849 | // if (spoly!=NULL) p_Content (spoly); // r? |
---|
850 | |
---|
851 | #ifdef PDEBUG |
---|
852 | p_Test (spoly, r); |
---|
853 | #endif |
---|
854 | |
---|
855 | return(spoly); |
---|
856 | } |
---|
857 | |
---|
858 | |
---|
859 | |
---|
860 | |
---|
861 | /*2 |
---|
862 | * reduction of p2 with p1 |
---|
863 | * do not destroy p1, but p2 |
---|
864 | * p1 divides p2 -> for use in NF algorithm |
---|
865 | */ |
---|
866 | poly sca_ReduceSpoly(const poly p1, poly p2, const ring r) |
---|
867 | { |
---|
868 | assume( rIsSCA(r) ); |
---|
869 | |
---|
870 | assume( p1 != NULL ); |
---|
871 | |
---|
872 | const long lCompP1 = p_GetComp (p1, r); |
---|
873 | const long lCompP2 = p_GetComp (p2, r); |
---|
874 | |
---|
875 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
876 | { |
---|
877 | #ifdef PDEBUG |
---|
878 | dReportError("sca_ReduceSpoly: different non-zero components!"); |
---|
879 | #endif |
---|
880 | return(NULL); |
---|
881 | } |
---|
882 | |
---|
883 | poly m = p_ISet (1, r); |
---|
884 | p_ExpVectorDiff (m, p2, p1, r); // m = lm(p2) / lm(p1) |
---|
885 | //p_Setm(m,r); |
---|
886 | #ifdef PDEBUG |
---|
887 | p_Test (m,r); |
---|
888 | #endif |
---|
889 | |
---|
890 | number C1 = n_Copy( p_GetCoeff(p1, r), r); |
---|
891 | number C2 = n_Copy( p_GetCoeff(p2, r), r); |
---|
892 | |
---|
893 | /* GCD stuff */ |
---|
894 | number C = n_Gcd(C1, C2, r); |
---|
895 | |
---|
896 | if (!n_IsOne(C, r)) |
---|
897 | { |
---|
898 | C1 = n_Div(C1, C, r); |
---|
899 | C2 = n_Div(C2, C, r); |
---|
900 | } |
---|
901 | n_Delete(&C,r); |
---|
902 | |
---|
903 | const int iSign = sca_Sign_mm_Mult_mm( m, p1, r ); |
---|
904 | |
---|
905 | if(iSign == 1) |
---|
906 | C2 = n_Neg(C2,r); |
---|
907 | |
---|
908 | p_SetCoeff(m, C2, r); |
---|
909 | |
---|
910 | #ifdef PDEBUG |
---|
911 | p_Test(m,r); |
---|
912 | #endif |
---|
913 | |
---|
914 | p2 = p_LmDeleteAndNext( p2, r ); |
---|
915 | |
---|
916 | p2 = p_Mult_nn(p2, C1, r); // p2 !!! |
---|
917 | n_Delete(&C1,r); |
---|
918 | |
---|
919 | poly T = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
920 | p_Delete(&m, r); |
---|
921 | |
---|
922 | p2 = p_Add_q(p2, T, r); |
---|
923 | |
---|
924 | if ( p2!=NULL ) p_Content(p2,r); |
---|
925 | |
---|
926 | #ifdef PDEBUG |
---|
927 | p_Test(p2,r); |
---|
928 | #endif |
---|
929 | |
---|
930 | return(p2); |
---|
931 | } |
---|
932 | |
---|
933 | /* |
---|
934 | void addLObject(LObject& h, kStrategy& strat) |
---|
935 | { |
---|
936 | if(h.IsNull()) return; |
---|
937 | |
---|
938 | strat->initEcart(&h); |
---|
939 | h.sev=0; // pGetShortExpVector(h.p); |
---|
940 | |
---|
941 | // add h into S and L |
---|
942 | int pos=posInS(strat, strat->sl, h.p, h.ecart); |
---|
943 | |
---|
944 | if ( (pos <= strat->sl) && (pComparePolys(h.p, strat->S[pos])) ) |
---|
945 | { |
---|
946 | if (TEST_OPT_PROT) |
---|
947 | PrintS("d\n"); |
---|
948 | } |
---|
949 | else |
---|
950 | { |
---|
951 | if (TEST_OPT_INTSTRATEGY) |
---|
952 | { |
---|
953 | p_Cleardenom(h.p, currRing); |
---|
954 | } |
---|
955 | else |
---|
956 | { |
---|
957 | pNorm(h.p); |
---|
958 | p_Content(h.p,currRing); |
---|
959 | } |
---|
960 | |
---|
961 | if ((strat->syzComp==0)||(!strat->homog)) |
---|
962 | { |
---|
963 | h.p = redtailBba(h.p,pos-1,strat); |
---|
964 | |
---|
965 | if (TEST_OPT_INTSTRATEGY) |
---|
966 | { |
---|
967 | // pCleardenom(h.p); |
---|
968 | p_Content(h.p,currRing); |
---|
969 | } |
---|
970 | else |
---|
971 | { |
---|
972 | pNorm(h.p); |
---|
973 | } |
---|
974 | } |
---|
975 | |
---|
976 | if(h.IsNull()) return; |
---|
977 | |
---|
978 | // statistic |
---|
979 | if (TEST_OPT_PROT) |
---|
980 | { |
---|
981 | PrintS("s\n"); |
---|
982 | } |
---|
983 | |
---|
984 | #ifdef KDEBUG |
---|
985 | if (TEST_OPT_DEBUG) |
---|
986 | { |
---|
987 | PrintS("new s:"); |
---|
988 | wrp(h.p); |
---|
989 | PrintLn(); |
---|
990 | } |
---|
991 | #endif |
---|
992 | |
---|
993 | enterpairs(h.p, strat->sl, h.ecart, 0, strat); |
---|
994 | |
---|
995 | pos=0; |
---|
996 | |
---|
997 | if (strat->sl!=-1) pos = posInS(strat, strat->sl, h.p, h.ecart); |
---|
998 | strat->enterS(h, pos, strat, -1); |
---|
999 | // enterT(h, strat); // ?! |
---|
1000 | |
---|
1001 | if (h.lcm!=NULL) pLmFree(h.lcm); |
---|
1002 | } |
---|
1003 | |
---|
1004 | |
---|
1005 | } |
---|
1006 | |
---|
1007 | */ |
---|
1008 | |
---|
1009 | |
---|
1010 | |
---|
1011 | ideal sca_gr_bba(const ideal F, const ideal Q, const intvec *, const intvec *, kStrategy strat, const ring _currRing) |
---|
1012 | { |
---|
1013 | /* |
---|
1014 | #if MYTEST |
---|
1015 | PrintS("<sca_gr_bba>\n"); |
---|
1016 | #endif |
---|
1017 | |
---|
1018 | assume(rIsSCA(currRing)); |
---|
1019 | |
---|
1020 | #ifndef NDEBUG |
---|
1021 | idTest(F); |
---|
1022 | idTest(Q); |
---|
1023 | #endif |
---|
1024 | |
---|
1025 | #ifdef HAVE_PLURAL |
---|
1026 | #if MYTEST |
---|
1027 | PrintS("currRing: \n"); |
---|
1028 | rWrite(currRing); |
---|
1029 | #ifdef RDEBUG |
---|
1030 | rDebugPrint(currRing); |
---|
1031 | #endif |
---|
1032 | |
---|
1033 | PrintS("F: \n"); |
---|
1034 | idPrint(F); |
---|
1035 | PrintS("Q: \n"); |
---|
1036 | idPrint(Q); |
---|
1037 | #endif |
---|
1038 | #endif |
---|
1039 | |
---|
1040 | |
---|
1041 | const unsigned int m_iFirstAltVar = scaFirstAltVar(currRing); |
---|
1042 | const unsigned int m_iLastAltVar = scaLastAltVar(currRing); |
---|
1043 | |
---|
1044 | ideal tempF = id_KillSquares(F, m_iFirstAltVar, m_iLastAltVar, currRing); |
---|
1045 | ideal tempQ = Q; |
---|
1046 | |
---|
1047 | if(Q == currQuotient) |
---|
1048 | tempQ = SCAQuotient(currRing); |
---|
1049 | |
---|
1050 | strat->z2homog = id_IsSCAHomogeneous(tempF, NULL, NULL, currRing); // wCx == wCy == NULL! |
---|
1051 | // redo: no_prod_crit |
---|
1052 | const BOOLEAN bIsSCA = rIsSCA(currRing) && strat->z2homog; // for Z_2 prod-crit |
---|
1053 | strat->no_prod_crit = ! bIsSCA; |
---|
1054 | |
---|
1055 | // strat->homog = strat->homog && strat->z2homog; // ? |
---|
1056 | |
---|
1057 | #if MYTEST |
---|
1058 | { |
---|
1059 | PrintS("ideal tempF: \n"); |
---|
1060 | idPrint(tempF); |
---|
1061 | PrintS("ideal tempQ: \n"); |
---|
1062 | idPrint(tempQ); |
---|
1063 | } |
---|
1064 | #endif |
---|
1065 | |
---|
1066 | #ifdef KDEBUG |
---|
1067 | om_Opts.MinTrack = 5; |
---|
1068 | #endif |
---|
1069 | |
---|
1070 | int srmax, lrmax; |
---|
1071 | int olddeg, reduc; |
---|
1072 | int red_result = 1; |
---|
1073 | // int hilbeledeg = 1, minimcnt = 0; |
---|
1074 | int hilbcount = 0; |
---|
1075 | |
---|
1076 | initBuchMoraCrit(strat); // set Gebauer, honey, sugarCrit |
---|
1077 | |
---|
1078 | nc_gr_initBba(tempF,strat); // set enterS, red, initEcart, initEcartPair |
---|
1079 | |
---|
1080 | initBuchMoraPos(strat); |
---|
1081 | |
---|
1082 | |
---|
1083 | // ?? set spSpolyShort, reduce ??? |
---|
1084 | |
---|
1085 | initBuchMora(tempF, tempQ, strat); // SCAQuotient(currRing) instead of Q == squares!!!!!!! |
---|
1086 | |
---|
1087 | strat->posInT=posInT110; // !!! |
---|
1088 | |
---|
1089 | srmax = strat->sl; |
---|
1090 | reduc = olddeg = lrmax = 0; |
---|
1091 | |
---|
1092 | |
---|
1093 | // compute------------------------------------------------------- |
---|
1094 | for(; strat->Ll >= 0; |
---|
1095 | #ifdef KDEBUG |
---|
1096 | strat->P.lcm = NULL, |
---|
1097 | #endif |
---|
1098 | kTest(strat) |
---|
1099 | ) |
---|
1100 | { |
---|
1101 | if (strat->Ll > lrmax) lrmax =strat->Ll;// stat. |
---|
1102 | |
---|
1103 | #ifdef KDEBUG |
---|
1104 | if (TEST_OPT_DEBUG) messageSets(strat); |
---|
1105 | #endif |
---|
1106 | |
---|
1107 | if (strat->Ll== 0) strat->interpt=TRUE; |
---|
1108 | |
---|
1109 | if (TEST_OPT_DEGBOUND |
---|
1110 | && ((strat->honey |
---|
1111 | && (strat->L[strat->Ll].ecart+pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)) |
---|
1112 | || ((!strat->honey) && (pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)))) |
---|
1113 | { |
---|
1114 | // stops computation if |
---|
1115 | // 24 IN test and the degree +ecart of L[strat->Ll] is bigger then |
---|
1116 | // a predefined number Kstd1_deg |
---|
1117 | while (strat->Ll >= 0) deleteInL(strat->L,&strat->Ll,strat->Ll,strat); |
---|
1118 | break; |
---|
1119 | } |
---|
1120 | |
---|
1121 | // picks the last element from the lazyset L |
---|
1122 | strat->P = strat->L[strat->Ll]; |
---|
1123 | strat->Ll--; |
---|
1124 | |
---|
1125 | //kTest(strat); |
---|
1126 | |
---|
1127 | // assume(pNext(strat->P.p) != strat->tail); // !??? |
---|
1128 | if(strat->P.IsNull()) continue; |
---|
1129 | |
---|
1130 | |
---|
1131 | if( pNext(strat->P.p) == strat->tail ) |
---|
1132 | { |
---|
1133 | // deletes the int spoly and computes SPoly |
---|
1134 | pLmFree(strat->P.p); // ??? |
---|
1135 | strat->P.p = nc_CreateSpoly(strat->P.p1, strat->P.p2, currRing); |
---|
1136 | } |
---|
1137 | |
---|
1138 | if(strat->P.IsNull()) continue; |
---|
1139 | |
---|
1140 | // poly save = NULL; |
---|
1141 | // |
---|
1142 | // if(pNext(strat->P.p) != NULL) |
---|
1143 | // save = p_Copy(strat->P.p, currRing); |
---|
1144 | |
---|
1145 | strat->initEcart(&strat->P); // remove it? |
---|
1146 | |
---|
1147 | if (TEST_OPT_PROT) |
---|
1148 | message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(), &olddeg,&reduc,strat, red_result); |
---|
1149 | |
---|
1150 | // reduction of the element chosen from L wrt S |
---|
1151 | strat->red(&strat->P,strat); |
---|
1152 | |
---|
1153 | if(strat->P.IsNull()) continue; |
---|
1154 | |
---|
1155 | addLObject(strat->P, strat); |
---|
1156 | |
---|
1157 | if (strat->sl > srmax) srmax = strat->sl; |
---|
1158 | |
---|
1159 | const poly save = strat->P.p; |
---|
1160 | |
---|
1161 | #ifdef PDEBUG |
---|
1162 | p_Test(save, currRing); |
---|
1163 | #endif |
---|
1164 | assume( save != NULL ); |
---|
1165 | |
---|
1166 | // SCA Specials: |
---|
1167 | |
---|
1168 | { |
---|
1169 | const poly p_next = pNext(save); |
---|
1170 | |
---|
1171 | if( p_next != NULL ) |
---|
1172 | for( unsigned int i = m_iFirstAltVar; i <= m_iLastAltVar; i++ ) |
---|
1173 | if( p_GetExp(save, i, currRing) != 0 ) |
---|
1174 | { |
---|
1175 | assume(p_GetExp(save, i, currRing) == 1); |
---|
1176 | |
---|
1177 | const poly tt = sca_pp_Mult_xi_pp(i, p_next, currRing); |
---|
1178 | |
---|
1179 | #ifdef PDEBUG |
---|
1180 | p_Test(tt, currRing); |
---|
1181 | #endif |
---|
1182 | |
---|
1183 | if( tt == NULL) continue; |
---|
1184 | |
---|
1185 | LObject h(tt); // h = x_i * P |
---|
1186 | |
---|
1187 | if (TEST_OPT_INTSTRATEGY) |
---|
1188 | { |
---|
1189 | // h.pCleardenom(); // also does a p_Content |
---|
1190 | p_Content(h.p,currRing); |
---|
1191 | } |
---|
1192 | else |
---|
1193 | { |
---|
1194 | h.pNorm(); |
---|
1195 | } |
---|
1196 | |
---|
1197 | strat->initEcart(&h); |
---|
1198 | |
---|
1199 | |
---|
1200 | // if (pOrdSgn==-1) |
---|
1201 | // { |
---|
1202 | // cancelunit(&h); // tries to cancel a unit |
---|
1203 | // deleteHC(&h, strat); |
---|
1204 | // } |
---|
1205 | |
---|
1206 | // if(h.IsNull()) continue; |
---|
1207 | |
---|
1208 | // if (TEST_OPT_PROT) |
---|
1209 | // message((strat->honey ? h.ecart : 0) + h.pFDeg(), &olddeg, &reduc, strat, red_result); |
---|
1210 | |
---|
1211 | // strat->red(&h, strat); // wrt S |
---|
1212 | // if(h.IsNull()) continue; |
---|
1213 | |
---|
1214 | // poly save = p_Copy(h.p, currRing); |
---|
1215 | |
---|
1216 | int pos; |
---|
1217 | |
---|
1218 | if (strat->Ll==-1) |
---|
1219 | pos =0; |
---|
1220 | else |
---|
1221 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
1222 | |
---|
1223 | h.sev = pGetShortExpVector(h.p); |
---|
1224 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
1225 | |
---|
1226 | // h.p = save; |
---|
1227 | // addLObject(h, strat); |
---|
1228 | |
---|
1229 | // if (strat->sl > srmax) srmax = strat->sl; |
---|
1230 | } |
---|
1231 | |
---|
1232 | // p_Delete( &save, currRing ); |
---|
1233 | } |
---|
1234 | |
---|
1235 | |
---|
1236 | } // for(;;) |
---|
1237 | |
---|
1238 | |
---|
1239 | #ifdef KDEBUG |
---|
1240 | if (TEST_OPT_DEBUG) messageSets(strat); |
---|
1241 | #endif |
---|
1242 | |
---|
1243 | if (TEST_OPT_REDSB){ |
---|
1244 | completeReduce(strat); // ??? |
---|
1245 | } |
---|
1246 | |
---|
1247 | // release temp data-------------------------------- |
---|
1248 | exitBuchMora(strat); |
---|
1249 | |
---|
1250 | if (TEST_OPT_WEIGHTM) |
---|
1251 | { |
---|
1252 | pFDeg=pFDegOld; |
---|
1253 | pLDeg=pLDegOld; |
---|
1254 | if (ecartWeights) |
---|
1255 | { |
---|
1256 | omFreeSize((ADDRESS)ecartWeights,(pVariables+1)*sizeof(int)); |
---|
1257 | ecartWeights=NULL; |
---|
1258 | } |
---|
1259 | } |
---|
1260 | |
---|
1261 | if (TEST_OPT_PROT) messageStat(srmax,lrmax,hilbcount,strat); |
---|
1262 | |
---|
1263 | if (tempQ!=NULL) updateResult(strat->Shdl,tempQ,strat); |
---|
1264 | |
---|
1265 | id_Delete(&tempF, currRing); |
---|
1266 | |
---|
1267 | |
---|
1268 | // complete reduction of the standard basis--------- |
---|
1269 | if (TEST_OPT_REDSB){ |
---|
1270 | ideal I = strat->Shdl; |
---|
1271 | ideal erg = kInterRedOld(I,tempQ); |
---|
1272 | assume(I!=erg); |
---|
1273 | id_Delete(&I, currRing); |
---|
1274 | strat->Shdl = erg; |
---|
1275 | } |
---|
1276 | |
---|
1277 | |
---|
1278 | #if MYTEST |
---|
1279 | // PrintS("</sca_gr_bba>\n"); |
---|
1280 | #endif |
---|
1281 | |
---|
1282 | return (strat->Shdl); |
---|
1283 | */ |
---|
1284 | } |
---|
1285 | |
---|
1286 | |
---|
1287 | |
---|
1288 | // should be used only inside nc_SetupQuotient! |
---|
1289 | // Check whether this our case: |
---|
1290 | // 1. rG is a commutative polynomial ring \otimes anticommutative algebra |
---|
1291 | // 2. factor ideal rGR->qideal contains squares of all alternating variables. |
---|
1292 | // |
---|
1293 | // if yes, make rGR a super-commutative algebra! |
---|
1294 | // NOTE: Factors of SuperCommutative Algebras are supported this way! |
---|
1295 | // |
---|
1296 | // rG == NULL means that there is no separate base G-algebra in this case take rGR == rG |
---|
1297 | |
---|
1298 | // special case: bCopy == true (default value: false) |
---|
1299 | // meaning: rGR copies structure from rG |
---|
1300 | // (maybe with some minor changes, which don't change the type!) |
---|
1301 | bool sca_SetupQuotient(ring rGR, ring rG, bool bCopy) |
---|
1302 | { |
---|
1303 | |
---|
1304 | ////////////////////////////////////////////////////////////////////////// |
---|
1305 | // checks... |
---|
1306 | ////////////////////////////////////////////////////////////////////////// |
---|
1307 | if( rG == NULL ) |
---|
1308 | rG = rGR; |
---|
1309 | |
---|
1310 | assume(rGR != NULL); |
---|
1311 | assume(rG != NULL); |
---|
1312 | assume(rIsPluralRing(rG)); |
---|
1313 | |
---|
1314 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1315 | PrintS("sca_SetupQuotient(rGR, rG, bCopy)"); |
---|
1316 | |
---|
1317 | { |
---|
1318 | PrintS("\nrG: \n"); rWrite(rG); |
---|
1319 | PrintS("\nrGR: \n"); rWrite(rGR); |
---|
1320 | PrintLn(); |
---|
1321 | } |
---|
1322 | #endif |
---|
1323 | |
---|
1324 | |
---|
1325 | if(bCopy) |
---|
1326 | { |
---|
1327 | if(rIsSCA(rG) && (rG != rGR)) |
---|
1328 | return sca_Force(rGR, scaFirstAltVar(rG), scaLastAltVar(rG)); |
---|
1329 | else |
---|
1330 | return false; |
---|
1331 | } |
---|
1332 | |
---|
1333 | assume(!bCopy); |
---|
1334 | |
---|
1335 | const int N = rG->N; |
---|
1336 | |
---|
1337 | if(N < 2) |
---|
1338 | return false; |
---|
1339 | |
---|
1340 | |
---|
1341 | // if( (ncRingType(rG) != nc_skew) || (ncRingType(rG) != nc_comm) ) |
---|
1342 | // return false; |
---|
1343 | |
---|
1344 | #if OUTPUT |
---|
1345 | PrintS("sca_SetupQuotient: qring?\n"); |
---|
1346 | #endif |
---|
1347 | |
---|
1348 | if(rGR->qideal == NULL) // there should be a factor! |
---|
1349 | return false; |
---|
1350 | |
---|
1351 | #if OUTPUT |
---|
1352 | PrintS("sca_SetupQuotient: qideal!!!\n"); |
---|
1353 | #endif |
---|
1354 | |
---|
1355 | // if((rG->qideal != NULL) && (rG != rGR) ) // we cannot change from factor to factor at the time, sorry! |
---|
1356 | // return false; |
---|
1357 | |
---|
1358 | |
---|
1359 | int iAltVarEnd = -1; |
---|
1360 | int iAltVarStart = N+1; |
---|
1361 | |
---|
1362 | const nc_struct* NC = rG->GetNC(); |
---|
1363 | const ring rBase = rG; //NC->basering; |
---|
1364 | const matrix C = NC->C; // live in rBase! |
---|
1365 | const matrix D = NC->D; // live in rBase! |
---|
1366 | |
---|
1367 | #if OUTPUT |
---|
1368 | PrintS("sca_SetupQuotient: AltVars?!\n"); |
---|
1369 | #endif |
---|
1370 | |
---|
1371 | for(int i = 1; i < N; i++) |
---|
1372 | { |
---|
1373 | for(int j = i + 1; j <= N; j++) |
---|
1374 | { |
---|
1375 | if( MATELEM(D,i,j) != NULL) // !!!??? |
---|
1376 | { |
---|
1377 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1378 | Print("Nonzero D[%d, %d]\n", i, j); |
---|
1379 | #endif |
---|
1380 | return false; |
---|
1381 | } |
---|
1382 | |
---|
1383 | |
---|
1384 | assume(MATELEM(C,i,j) != NULL); // after CallPlural! |
---|
1385 | number c = p_GetCoeff(MATELEM(C,i,j), rBase); |
---|
1386 | |
---|
1387 | if( n_IsMOne(c, rBase) ) // !!!??? |
---|
1388 | { |
---|
1389 | if( i < iAltVarStart) |
---|
1390 | iAltVarStart = i; |
---|
1391 | |
---|
1392 | if( j > iAltVarEnd) |
---|
1393 | iAltVarEnd = j; |
---|
1394 | } else |
---|
1395 | { |
---|
1396 | if( !n_IsOne(c, rBase) ) |
---|
1397 | { |
---|
1398 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1399 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1400 | #endif |
---|
1401 | return false; |
---|
1402 | } |
---|
1403 | } |
---|
1404 | } |
---|
1405 | } |
---|
1406 | |
---|
1407 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1408 | Print("AltVars?1: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1409 | #endif |
---|
1410 | |
---|
1411 | |
---|
1412 | if( (iAltVarEnd == -1) || (iAltVarStart == (N+1)) ) |
---|
1413 | return false; // either no alternating varables, or a single one => we are in commutative case! |
---|
1414 | |
---|
1415 | |
---|
1416 | for(int i = 1; i < N; i++) |
---|
1417 | { |
---|
1418 | for(int j = i + 1; j <= N; j++) |
---|
1419 | { |
---|
1420 | assume(MATELEM(C,i,j) != NULL); // after CallPlural! |
---|
1421 | number c = p_GetCoeff(MATELEM(C,i,j), rBase); |
---|
1422 | |
---|
1423 | if( (iAltVarStart <= i) && (j <= iAltVarEnd) ) // S <= i < j <= E |
---|
1424 | { // anticommutative part |
---|
1425 | if( !n_IsMOne(c, rBase) ) |
---|
1426 | { |
---|
1427 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1428 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1429 | #endif |
---|
1430 | return false; |
---|
1431 | } |
---|
1432 | } else |
---|
1433 | { // should commute |
---|
1434 | if( !n_IsOne(c, rBase) ) |
---|
1435 | { |
---|
1436 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1437 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1438 | #endif |
---|
1439 | return false; |
---|
1440 | } |
---|
1441 | } |
---|
1442 | } |
---|
1443 | } |
---|
1444 | |
---|
1445 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1446 | Print("AltVars!?: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1447 | #endif |
---|
1448 | |
---|
1449 | assume( 1 <= iAltVarStart ); |
---|
1450 | assume( iAltVarStart < iAltVarEnd ); |
---|
1451 | assume( iAltVarEnd <= N ); |
---|
1452 | |
---|
1453 | |
---|
1454 | // ring rSaveRing = assureCurrentRing(rG); |
---|
1455 | |
---|
1456 | |
---|
1457 | assume(rGR->qideal != NULL); |
---|
1458 | assume(rGR->N == rG->N); |
---|
1459 | // assume(rG->qideal == NULL); // ? |
---|
1460 | |
---|
1461 | const ideal idQuotient = rGR->qideal; |
---|
1462 | |
---|
1463 | |
---|
1464 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1465 | PrintS("Analyzing quotient ideal:\n"); |
---|
1466 | idPrint(idQuotient); // in rG!!! |
---|
1467 | #endif |
---|
1468 | |
---|
1469 | |
---|
1470 | // check for |
---|
1471 | // y_{iAltVarStart}^2, y_{iAltVarStart+1}^2, \ldots, y_{iAltVarEnd}^2 (iAltVarEnd > iAltVarStart) |
---|
1472 | // to be within quotient ideal. |
---|
1473 | |
---|
1474 | bool bSCA = true; |
---|
1475 | |
---|
1476 | int b = N+1; |
---|
1477 | int e = -1; |
---|
1478 | |
---|
1479 | if(rIsSCA(rG)) |
---|
1480 | { |
---|
1481 | b = si_min(b, scaFirstAltVar(rG)); |
---|
1482 | e = si_max(e, scaLastAltVar(rG)); |
---|
1483 | |
---|
1484 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1485 | Print("AltVars!?: [%d, %d]\n", b, e); |
---|
1486 | #endif |
---|
1487 | } |
---|
1488 | |
---|
1489 | for ( int i = iAltVarStart; (i <= iAltVarEnd) && bSCA; i++ ) |
---|
1490 | if( (i < b) || (i > e) ) // otherwise it's ok since rG is an SCA! |
---|
1491 | { |
---|
1492 | poly square = p_One( rG); |
---|
1493 | p_SetExp(square, i, 2, rG); // square = var(i)^2. |
---|
1494 | p_Setm(square, rG); |
---|
1495 | |
---|
1496 | // square = NF( var(i)^2 | Q ) |
---|
1497 | // NOTE: rSaveRing == currRing now! |
---|
1498 | // NOTE: there is no better way to check this in general! |
---|
1499 | extern poly kNF(ideal I, ideal Q, poly f, int a, int b, const ring r); |
---|
1500 | |
---|
1501 | square = kNF(idQuotient, NULL, square, 0, 1, rG); // must ran in currRing == rG! |
---|
1502 | |
---|
1503 | if( square != NULL ) // var(i)^2 is not in Q? |
---|
1504 | { |
---|
1505 | p_Delete(&square, rG); |
---|
1506 | bSCA = false; |
---|
1507 | break; |
---|
1508 | } |
---|
1509 | } |
---|
1510 | |
---|
1511 | // assureCurrentRing(rSaveRing); |
---|
1512 | |
---|
1513 | if(!bSCA) return false; |
---|
1514 | |
---|
1515 | |
---|
1516 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1517 | Print("ScaVars!: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1518 | #endif |
---|
1519 | |
---|
1520 | |
---|
1521 | ////////////////////////////////////////////////////////////////////////// |
---|
1522 | // ok... here we go. let's setup it!!! |
---|
1523 | ////////////////////////////////////////////////////////////////////////// |
---|
1524 | ideal tempQ = id_KillSquares(idQuotient, iAltVarStart, iAltVarEnd, rG); // in rG!!! |
---|
1525 | |
---|
1526 | |
---|
1527 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1528 | PrintS("Quotient: \n"); |
---|
1529 | iiWriteMatrix((matrix)idQuotient,"__",1); |
---|
1530 | PrintS("tempSCAQuotient: \n"); |
---|
1531 | iiWriteMatrix((matrix)tempQ,"__",1); |
---|
1532 | #endif |
---|
1533 | |
---|
1534 | idSkipZeroes( tempQ ); |
---|
1535 | |
---|
1536 | ncRingType( rGR, nc_exterior ); |
---|
1537 | |
---|
1538 | scaFirstAltVar( rGR, iAltVarStart ); |
---|
1539 | scaLastAltVar( rGR, iAltVarEnd ); |
---|
1540 | |
---|
1541 | if( idIs0(tempQ) ) |
---|
1542 | rGR->GetNC()->SCAQuotient() = NULL; |
---|
1543 | else |
---|
1544 | rGR->GetNC()->SCAQuotient() = idrMoveR(tempQ, rG, rGR); // deletes tempQ! |
---|
1545 | |
---|
1546 | nc_p_ProcsSet(rGR, rGR->p_Procs); // !!!!!!!!!!!!!!!!! |
---|
1547 | |
---|
1548 | |
---|
1549 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1550 | PrintS("SCAQuotient: \n"); |
---|
1551 | if(tempQ != NULL) |
---|
1552 | iiWriteMatrix((matrix)tempQ,"__",1); |
---|
1553 | else |
---|
1554 | PrintS("(NULL)\n"); |
---|
1555 | #endif |
---|
1556 | |
---|
1557 | return true; |
---|
1558 | } |
---|
1559 | |
---|
1560 | |
---|
1561 | bool sca_Force(ring rGR, int b, int e) |
---|
1562 | { |
---|
1563 | assume(rGR != NULL); |
---|
1564 | assume(rIsPluralRing(rGR)); |
---|
1565 | assume(!rIsSCA(rGR)); |
---|
1566 | |
---|
1567 | const int N = rGR->N; |
---|
1568 | |
---|
1569 | // ring rSaveRing = currRing; |
---|
1570 | // if(rSaveRing != rGR) |
---|
1571 | // rChangeCurrRing(rGR); |
---|
1572 | |
---|
1573 | const ideal idQuotient = rGR->qideal; |
---|
1574 | |
---|
1575 | ideal tempQ = idQuotient; |
---|
1576 | |
---|
1577 | if( b <= N && e >= 1 ) |
---|
1578 | tempQ = id_KillSquares(idQuotient, b, e, rGR); |
---|
1579 | |
---|
1580 | idSkipZeroes( tempQ ); |
---|
1581 | |
---|
1582 | ncRingType( rGR, nc_exterior ); |
---|
1583 | |
---|
1584 | if( idIs0(tempQ) ) |
---|
1585 | rGR->GetNC()->SCAQuotient() = NULL; |
---|
1586 | else |
---|
1587 | rGR->GetNC()->SCAQuotient() = tempQ; |
---|
1588 | |
---|
1589 | |
---|
1590 | scaFirstAltVar( rGR, b ); |
---|
1591 | scaLastAltVar( rGR, e ); |
---|
1592 | |
---|
1593 | |
---|
1594 | nc_p_ProcsSet(rGR, rGR->p_Procs); |
---|
1595 | |
---|
1596 | // if(rSaveRing != rGR) |
---|
1597 | // rChangeCurrRing(rSaveRing); |
---|
1598 | |
---|
1599 | return true; |
---|
1600 | } |
---|
1601 | |
---|
1602 | // return x_i * pPoly; preserve pPoly. |
---|
1603 | poly sca_pp_Mult_xi_pp(unsigned int i, const poly pPoly, const ring rRing) |
---|
1604 | { |
---|
1605 | assume(1 <= i); |
---|
1606 | assume(i <= (unsigned int)rRing->N); |
---|
1607 | |
---|
1608 | if(rIsSCA(rRing)) |
---|
1609 | return sca_xi_Mult_pp(i, pPoly, rRing); |
---|
1610 | |
---|
1611 | |
---|
1612 | |
---|
1613 | poly xi = p_One( rRing); |
---|
1614 | p_SetExp(xi, i, 1, rRing); |
---|
1615 | p_Setm(xi, rRing); |
---|
1616 | |
---|
1617 | poly pResult = pp_Mult_qq(xi, pPoly, rRing); |
---|
1618 | |
---|
1619 | p_Delete( &xi, rRing); |
---|
1620 | |
---|
1621 | return pResult; |
---|
1622 | |
---|
1623 | } |
---|
1624 | |
---|
1625 | |
---|
1626 | /////////////////////////////////////////////////////////////////////////////////////// |
---|
1627 | //************* SCA BBA *************************************************************// |
---|
1628 | /////////////////////////////////////////////////////////////////////////////////////// |
---|
1629 | |
---|
1630 | // Under development!!! |
---|
1631 | ideal sca_bba (const ideal F, const ideal Q, const intvec *w, const intvec * /*hilb*/, kStrategy strat) |
---|
1632 | { |
---|
1633 | /* |
---|
1634 | #if MYTEST |
---|
1635 | PrintS("\n\n<sca_bba>\n\n"); |
---|
1636 | #endif |
---|
1637 | |
---|
1638 | assume(rIsSCA(currRing)); |
---|
1639 | |
---|
1640 | #ifndef NDEBUG |
---|
1641 | idTest(F); |
---|
1642 | idTest(Q); |
---|
1643 | #endif |
---|
1644 | |
---|
1645 | #if MYTEST |
---|
1646 | PrintS("\ncurrRing: \n"); |
---|
1647 | rWrite(currRing); |
---|
1648 | #ifdef RDEBUG |
---|
1649 | // rDebugPrint(currRing); |
---|
1650 | #endif |
---|
1651 | |
---|
1652 | PrintS("\n\nF: \n"); |
---|
1653 | idPrint(F); |
---|
1654 | PrintS("\n\nQ: \n"); |
---|
1655 | idPrint(Q); |
---|
1656 | |
---|
1657 | PrintLn(); |
---|
1658 | #endif |
---|
1659 | |
---|
1660 | |
---|
1661 | const unsigned int m_iFirstAltVar = scaFirstAltVar(currRing); |
---|
1662 | const unsigned int m_iLastAltVar = scaLastAltVar(currRing); |
---|
1663 | |
---|
1664 | ideal tempF = id_KillSquares(F, m_iFirstAltVar, m_iLastAltVar, currRing); |
---|
1665 | |
---|
1666 | ideal tempQ = Q; |
---|
1667 | |
---|
1668 | if(Q == currQuotient) |
---|
1669 | tempQ = SCAQuotient(currRing); |
---|
1670 | |
---|
1671 | // Q or tempQ will not be used below :((( |
---|
1672 | |
---|
1673 | |
---|
1674 | #if MYTEST |
---|
1675 | |
---|
1676 | PrintS("tempF: \n"); |
---|
1677 | idPrint(tempF); |
---|
1678 | PrintS("tempQ: \n"); |
---|
1679 | idPrint(tempQ); |
---|
1680 | #endif |
---|
1681 | |
---|
1682 | strat->z2homog = id_IsSCAHomogeneous(tempF, NULL, NULL, currRing); // wCx == wCy == NULL! |
---|
1683 | // redo no_prod_crit: |
---|
1684 | const BOOLEAN bIsSCA = rIsSCA(currRing) && strat->z2homog; // for Z_2 prod-crit |
---|
1685 | strat->no_prod_crit = ! bIsSCA; |
---|
1686 | |
---|
1687 | // strat->homog = strat->homog && strat->z2homog; // ? |
---|
1688 | |
---|
1689 | |
---|
1690 | |
---|
1691 | #ifdef KDEBUG |
---|
1692 | om_Opts.MinTrack = 5; |
---|
1693 | #endif |
---|
1694 | |
---|
1695 | int srmax, lrmax, red_result = 1; |
---|
1696 | int olddeg, reduc; |
---|
1697 | |
---|
1698 | // int hilbeledeg = 1, minimcnt = 0; |
---|
1699 | int hilbcount = 0; |
---|
1700 | |
---|
1701 | BOOLEAN withT = FALSE; |
---|
1702 | |
---|
1703 | initBuchMoraCrit(strat); // sets Gebauer, honey, sugarCrit // sca - ok??? |
---|
1704 | initBuchMoraPos(strat); // sets strat->posInL, strat->posInT // check!! (Plural's: ) |
---|
1705 | |
---|
1706 | // initHilbCrit(F, Q, &hilb, strat); |
---|
1707 | |
---|
1708 | // nc_gr_initBba(F,strat); |
---|
1709 | initBba(tempF, strat); // set enterS, red, initEcart, initEcartPair |
---|
1710 | |
---|
1711 | // set enterS, spSpolyShort, reduce, red, initEcart, initEcartPair |
---|
1712 | // ?? set spSpolyShort, reduce ??? |
---|
1713 | initBuchMora(tempF, tempQ, strat); // tempQ = Q without squares!!! |
---|
1714 | |
---|
1715 | // if (strat->minim>0) strat->M = idInit(IDELEMS(F),F->rank); |
---|
1716 | |
---|
1717 | srmax = strat->sl; |
---|
1718 | reduc = olddeg = lrmax = 0; |
---|
1719 | |
---|
1720 | #define NO_BUCKETS |
---|
1721 | |
---|
1722 | #ifndef NO_BUCKETS |
---|
1723 | if (!TEST_OPT_NOT_BUCKETS) |
---|
1724 | strat->use_buckets = 1; |
---|
1725 | #endif |
---|
1726 | |
---|
1727 | // redtailBBa against T for inhomogenous input |
---|
1728 | if (!TEST_OPT_OLDSTD) |
---|
1729 | withT = ! strat->homog; |
---|
1730 | |
---|
1731 | // strat->posInT = posInT_pLength; |
---|
1732 | kTest_TS(strat); |
---|
1733 | |
---|
1734 | #undef HAVE_TAIL_RING |
---|
1735 | |
---|
1736 | #ifdef HAVE_TAIL_RING |
---|
1737 | if(!idIs0(F) &&(!rField_is_Ring())) // create strong gcd poly computes with tailring and S[i] ->to be fixed |
---|
1738 | kStratInitChangeTailRing(strat); |
---|
1739 | #endif |
---|
1740 | if (BVERBOSE(23)) |
---|
1741 | { |
---|
1742 | if (test_PosInT!=NULL) strat->posInT=test_PosInT; |
---|
1743 | if (test_PosInL!=NULL) strat->posInL=test_PosInL; |
---|
1744 | kDebugPrint(strat); |
---|
1745 | } |
---|
1746 | |
---|
1747 | |
---|
1748 | /////////////////////////////////////////////////////////////// |
---|
1749 | // SCA: |
---|
1750 | |
---|
1751 | // due to std( SB, p). |
---|
1752 | // Note that after initBuchMora :: initSSpecial all these additional |
---|
1753 | // elements are in S and T (and some pairs are in L, which also has no initiall |
---|
1754 | // elements!!!) |
---|
1755 | if(TEST_OPT_SB_1) |
---|
1756 | { |
---|
1757 | // For all additional elements... |
---|
1758 | for (int iNewElement = strat->newIdeal; iNewElement < IDELEMS(tempF); iNewElement++) |
---|
1759 | { |
---|
1760 | const poly pSave = tempF->m[iNewElement]; |
---|
1761 | |
---|
1762 | if( pSave != NULL ) |
---|
1763 | { |
---|
1764 | // tempF->m[iNewElement] = NULL; |
---|
1765 | |
---|
1766 | const poly p_next = pNext(pSave); |
---|
1767 | |
---|
1768 | if(p_next != NULL) |
---|
1769 | for( unsigned int i = m_iFirstAltVar; i <= m_iLastAltVar; i++ ) |
---|
1770 | if( p_GetExp(pSave, i, currRing) != 0 ) |
---|
1771 | { |
---|
1772 | assume(p_GetExp(pSave, i, currRing) == 1); |
---|
1773 | |
---|
1774 | const poly p_new = sca_pp_Mult_xi_pp(i, p_next, currRing); |
---|
1775 | |
---|
1776 | #ifdef PDEBUG |
---|
1777 | p_Test(p_new, currRing); |
---|
1778 | #endif |
---|
1779 | |
---|
1780 | if( p_new == NULL) continue; |
---|
1781 | |
---|
1782 | LObject h(p_new); // h = x_i * strat->P |
---|
1783 | h.is_special = TRUE; |
---|
1784 | |
---|
1785 | if (TEST_OPT_INTSTRATEGY) |
---|
1786 | h.pCleardenom(); // also does a p_Content |
---|
1787 | else |
---|
1788 | h.pNorm(); |
---|
1789 | |
---|
1790 | strat->initEcart(&h); |
---|
1791 | h.sev = pGetShortExpVector(h.p); |
---|
1792 | |
---|
1793 | int pos = 0; |
---|
1794 | |
---|
1795 | if (strat->Ll != -1) |
---|
1796 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
1797 | |
---|
1798 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
1799 | } |
---|
1800 | } |
---|
1801 | } |
---|
1802 | } |
---|
1803 | |
---|
1804 | // compute------------------------------------------------------- |
---|
1805 | while (strat->Ll >= 0) |
---|
1806 | { |
---|
1807 | if (strat->Ll > lrmax) lrmax =strat->Ll;// stat. |
---|
1808 | |
---|
1809 | #ifdef KDEBUG |
---|
1810 | // loop_count++; |
---|
1811 | if (TEST_OPT_DEBUG) messageSets(strat); |
---|
1812 | #endif |
---|
1813 | |
---|
1814 | if (strat->Ll== 0) strat->interpt=TRUE; |
---|
1815 | |
---|
1816 | if (TEST_OPT_DEGBOUND |
---|
1817 | && ((strat->honey && (strat->L[strat->Ll].ecart+pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)) |
---|
1818 | || ((!strat->honey) && (pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)))) |
---|
1819 | { |
---|
1820 | |
---|
1821 | #ifdef KDEBUG |
---|
1822 | // if (TEST_OPT_DEBUG){PrintS("^^^^?");} |
---|
1823 | #endif |
---|
1824 | |
---|
1825 | // *stops computation if |
---|
1826 | // * 24 IN test and the degree +ecart of L[strat->Ll] is bigger then |
---|
1827 | // *a predefined number Kstd1_deg |
---|
1828 | while ((strat->Ll >= 0) |
---|
1829 | && ( (strat->homog==isHomog) || strat->L[strat->Ll].is_special || ((strat->L[strat->Ll].p1!=NULL) && (strat->L[strat->Ll].p2!=NULL)) ) |
---|
1830 | && ((strat->honey && (strat->L[strat->Ll].ecart+pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)) |
---|
1831 | || ((!strat->honey) && (pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))) |
---|
1832 | ) |
---|
1833 | { |
---|
1834 | #ifdef KDEBUG |
---|
1835 | // if (TEST_OPT_DEBUG){PrintS("^^^^^^^^^^^^!!!!");} |
---|
1836 | #endif |
---|
1837 | deleteInL(strat->L,&strat->Ll,strat->Ll,strat); |
---|
1838 | // if (TEST_OPT_PROT) PrintS("^!"); |
---|
1839 | } |
---|
1840 | if (strat->Ll<0) break; |
---|
1841 | else strat->noClearS=TRUE; |
---|
1842 | } |
---|
1843 | |
---|
1844 | // picks the last element from the lazyset L |
---|
1845 | strat->P = strat->L[strat->Ll]; |
---|
1846 | strat->Ll--; |
---|
1847 | |
---|
1848 | |
---|
1849 | // assume(pNext(strat->P.p) != strat->tail); |
---|
1850 | |
---|
1851 | if(strat->P.IsNull()) continue; |
---|
1852 | |
---|
1853 | if (pNext(strat->P.p) == strat->tail) |
---|
1854 | { |
---|
1855 | // deletes the short spoly |
---|
1856 | pLmFree(strat->P.p); |
---|
1857 | |
---|
1858 | strat->P.p = nc_CreateSpoly(strat->P.p1, strat->P.p2, currRing); |
---|
1859 | if (strat->P.p!=NULL) strat->initEcart(&strat->P); |
---|
1860 | }// else |
---|
1861 | |
---|
1862 | |
---|
1863 | if(strat->P.IsNull()) continue; |
---|
1864 | |
---|
1865 | if (strat->P.p1 == NULL) |
---|
1866 | { |
---|
1867 | // if (strat->minim > 0) |
---|
1868 | // strat->P.p2=p_Copy(strat->P.p, currRing, strat->tailRing); |
---|
1869 | |
---|
1870 | |
---|
1871 | // for input polys, prepare reduction |
---|
1872 | strat->P.PrepareRed(strat->use_buckets); |
---|
1873 | } |
---|
1874 | |
---|
1875 | if (TEST_OPT_PROT) |
---|
1876 | message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(), |
---|
1877 | &olddeg,&reduc,strat, red_result); |
---|
1878 | |
---|
1879 | // reduction of the element choosen from L |
---|
1880 | red_result = strat->red(&strat->P,strat); |
---|
1881 | |
---|
1882 | |
---|
1883 | // reduction to non-zero new poly |
---|
1884 | if (red_result == 1) |
---|
1885 | { |
---|
1886 | // statistic |
---|
1887 | if (TEST_OPT_PROT) PrintS("s"); |
---|
1888 | |
---|
1889 | // get the polynomial (canonicalize bucket, make sure P.p is set) |
---|
1890 | strat->P.GetP(strat->lmBin); |
---|
1891 | |
---|
1892 | int pos = posInS(strat,strat->sl,strat->P.p,strat->P.ecart); |
---|
1893 | |
---|
1894 | // reduce the tail and normalize poly |
---|
1895 | if (TEST_OPT_INTSTRATEGY) |
---|
1896 | { |
---|
1897 | strat->P.pCleardenom(); |
---|
1898 | if ((TEST_OPT_REDSB)||(TEST_OPT_REDTAIL)) |
---|
1899 | { |
---|
1900 | strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT); // !!! |
---|
1901 | strat->P.pCleardenom(); |
---|
1902 | } |
---|
1903 | } |
---|
1904 | else |
---|
1905 | { |
---|
1906 | strat->P.pNorm(); |
---|
1907 | if ((TEST_OPT_REDSB)||(TEST_OPT_REDTAIL)) |
---|
1908 | strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT); |
---|
1909 | } |
---|
1910 | strat->P.is_normalized=nIsOne(pGetCoeff(strat->P.p)); |
---|
1911 | |
---|
1912 | #ifdef KDEBUG |
---|
1913 | if (TEST_OPT_DEBUG){PrintS(" ns:");p_wrp(strat->P.p,currRing);PrintLn();} |
---|
1914 | #endif |
---|
1915 | |
---|
1916 | // // min_std stuff |
---|
1917 | // if ((strat->P.p1==NULL) && (strat->minim>0)) |
---|
1918 | // { |
---|
1919 | // if (strat->minim==1) |
---|
1920 | // { |
---|
1921 | // strat->M->m[minimcnt]=p_Copy(strat->P.p,currRing,strat->tailRing); |
---|
1922 | // p_Delete(&strat->P.p2, currRing, strat->tailRing); |
---|
1923 | // } |
---|
1924 | // else |
---|
1925 | // { |
---|
1926 | // strat->M->m[minimcnt]=strat->P.p2; |
---|
1927 | // strat->P.p2=NULL; |
---|
1928 | // } |
---|
1929 | // if (strat->tailRing!=currRing && pNext(strat->M->m[minimcnt])!=NULL) |
---|
1930 | // pNext(strat->M->m[minimcnt]) |
---|
1931 | // = strat->p_shallow_copy_delete(pNext(strat->M->m[minimcnt]), |
---|
1932 | // strat->tailRing, currRing, |
---|
1933 | // currRing->PolyBin); |
---|
1934 | // minimcnt++; |
---|
1935 | // } |
---|
1936 | |
---|
1937 | // enter into S, L, and T |
---|
1938 | //if(withT) |
---|
1939 | enterT(strat->P, strat); |
---|
1940 | |
---|
1941 | // L |
---|
1942 | enterpairs(strat->P.p,strat->sl,strat->P.ecart,pos,strat, strat->tl); |
---|
1943 | |
---|
1944 | // posInS only depends on the leading term |
---|
1945 | strat->enterS(strat->P, pos, strat, strat->tl); |
---|
1946 | |
---|
1947 | // if (hilb!=NULL) khCheck(Q,w,hilb,hilbeledeg,hilbcount,strat); |
---|
1948 | |
---|
1949 | // Print("[%d]",hilbeledeg); |
---|
1950 | if (strat->P.lcm!=NULL) pLmFree(strat->P.lcm); |
---|
1951 | |
---|
1952 | if (strat->sl>srmax) srmax = strat->sl; |
---|
1953 | |
---|
1954 | // ////////////////////////////////////////////////////////// |
---|
1955 | // SCA: |
---|
1956 | const poly pSave = strat->P.p; |
---|
1957 | const poly p_next = pNext(pSave); |
---|
1958 | |
---|
1959 | // if(0) |
---|
1960 | if( p_next != NULL ) |
---|
1961 | for( unsigned int i = m_iFirstAltVar; i <= m_iLastAltVar; i++ ) |
---|
1962 | if( p_GetExp(pSave, i, currRing) != 0 ) |
---|
1963 | { |
---|
1964 | assume(p_GetExp(pSave, i, currRing) == 1); |
---|
1965 | const poly p_new = sca_pp_Mult_xi_pp(i, p_next, currRing); |
---|
1966 | |
---|
1967 | #ifdef PDEBUG |
---|
1968 | p_Test(p_new, currRing); |
---|
1969 | #endif |
---|
1970 | |
---|
1971 | if( p_new == NULL) continue; |
---|
1972 | |
---|
1973 | LObject h(p_new); // h = x_i * strat->P |
---|
1974 | |
---|
1975 | h.is_special = TRUE; |
---|
1976 | |
---|
1977 | if (TEST_OPT_INTSTRATEGY) |
---|
1978 | { |
---|
1979 | // p_Content(h.p); |
---|
1980 | h.pCleardenom(); // also does a p_Content |
---|
1981 | } |
---|
1982 | else |
---|
1983 | { |
---|
1984 | h.pNorm(); |
---|
1985 | } |
---|
1986 | |
---|
1987 | strat->initEcart(&h); |
---|
1988 | h.sev = pGetShortExpVector(h.p); |
---|
1989 | |
---|
1990 | int pos = 0; |
---|
1991 | |
---|
1992 | if (strat->Ll != -1) |
---|
1993 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
1994 | |
---|
1995 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
1996 | |
---|
1997 | |
---|
1998 | |
---|
1999 | |
---|
2000 | #if 0 |
---|
2001 | h.sev = pGetShortExpVector(h.p); |
---|
2002 | strat->initEcart(&h); |
---|
2003 | |
---|
2004 | h.PrepareRed(strat->use_buckets); |
---|
2005 | |
---|
2006 | // reduction of the element choosen from L(?) |
---|
2007 | red_result = strat->red(&h,strat); |
---|
2008 | |
---|
2009 | // reduction to non-zero new poly |
---|
2010 | if (red_result != 1) continue; |
---|
2011 | |
---|
2012 | |
---|
2013 | int pos = posInS(strat,strat->sl,h.p,h.ecart); |
---|
2014 | |
---|
2015 | // reduce the tail and normalize poly |
---|
2016 | if (TEST_OPT_INTSTRATEGY) |
---|
2017 | { |
---|
2018 | h.pCleardenom(); |
---|
2019 | if ((TEST_OPT_REDSB)||(TEST_OPT_REDTAIL)) |
---|
2020 | { |
---|
2021 | h.p = redtailBba(&(h),pos-1,strat, withT); // !!! |
---|
2022 | h.pCleardenom(); |
---|
2023 | } |
---|
2024 | } |
---|
2025 | else |
---|
2026 | { |
---|
2027 | h.pNorm(); |
---|
2028 | if ((TEST_OPT_REDSB)||(TEST_OPT_REDTAIL)) |
---|
2029 | h.p = redtailBba(&(h),pos-1,strat, withT); |
---|
2030 | } |
---|
2031 | |
---|
2032 | #ifdef KDEBUG |
---|
2033 | if (TEST_OPT_DEBUG){PrintS(" N:");h.wrp();PrintLn();} |
---|
2034 | #endif |
---|
2035 | |
---|
2036 | // h.PrepareRed(strat->use_buckets); // ??? |
---|
2037 | |
---|
2038 | h.sev = pGetShortExpVector(h.p); |
---|
2039 | strat->initEcart(&h); |
---|
2040 | |
---|
2041 | if (strat->Ll==-1) |
---|
2042 | pos = 0; |
---|
2043 | else |
---|
2044 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
2045 | |
---|
2046 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
2047 | // the end of "#if 0" (comment) |
---|
2048 | #endif |
---|
2049 | |
---|
2050 | } // for all x_i \in Ann(lm(P)) |
---|
2051 | } // if red(P) != NULL |
---|
2052 | |
---|
2053 | // else if (strat->P.p1 == NULL && strat->minim > 0) |
---|
2054 | // { |
---|
2055 | // p_Delete(&strat->P.p2, currRing, strat->tailRing); |
---|
2056 | // } |
---|
2057 | |
---|
2058 | #ifdef KDEBUG |
---|
2059 | // memset(&(strat->P), 0, sizeof(strat->P)); |
---|
2060 | #endif |
---|
2061 | |
---|
2062 | kTest_TS(strat); // even of T is not used! |
---|
2063 | |
---|
2064 | // Print("\n$\n"); |
---|
2065 | |
---|
2066 | } |
---|
2067 | |
---|
2068 | #ifdef KDEBUG |
---|
2069 | if (TEST_OPT_DEBUG) messageSets(strat); |
---|
2070 | #endif |
---|
2071 | |
---|
2072 | // complete reduction of the standard basis--------- |
---|
2073 | |
---|
2074 | if (TEST_OPT_REDSB) |
---|
2075 | { |
---|
2076 | completeReduce(strat); |
---|
2077 | } |
---|
2078 | |
---|
2079 | //release temp data-------------------------------- |
---|
2080 | |
---|
2081 | exitBuchMora(strat); // cleanT! |
---|
2082 | |
---|
2083 | id_Delete(&tempF, currRing); |
---|
2084 | |
---|
2085 | if (TEST_OPT_WEIGHTM) |
---|
2086 | { |
---|
2087 | pRestoreDegProcs(pFDegOld, pLDegOld); |
---|
2088 | if (ecartWeights) |
---|
2089 | { |
---|
2090 | omFreeSize((ADDRESS)ecartWeights,(pVariables+1)*sizeof(short)); |
---|
2091 | ecartWeights=NULL; |
---|
2092 | } |
---|
2093 | } |
---|
2094 | |
---|
2095 | if (TEST_OPT_PROT) messageStat(srmax,lrmax,hilbcount,strat); |
---|
2096 | |
---|
2097 | |
---|
2098 | |
---|
2099 | if (tempQ!=NULL) updateResult(strat->Shdl,tempQ,strat); |
---|
2100 | |
---|
2101 | |
---|
2102 | if (TEST_OPT_REDSB) // ??? |
---|
2103 | { |
---|
2104 | // must be at the very end (after exitBuchMora) as it changes the S set!!! |
---|
2105 | ideal I = strat->Shdl; |
---|
2106 | ideal erg = kInterRedOld(I,tempQ); |
---|
2107 | assume(I!=erg); |
---|
2108 | id_Delete(&I, currRing); |
---|
2109 | strat->Shdl = erg; |
---|
2110 | } |
---|
2111 | |
---|
2112 | #if MYTEST |
---|
2113 | PrintS("\n\n</sca_bba>\n\n"); |
---|
2114 | #endif |
---|
2115 | |
---|
2116 | return (strat->Shdl); |
---|
2117 | */ |
---|
2118 | } |
---|
2119 | |
---|
2120 | // ////////////////////////////////////////////////////////////////////////////// |
---|
2121 | // sca mora... |
---|
2122 | |
---|
2123 | /* |
---|
2124 | // returns TRUE if mora should use buckets, false otherwise |
---|
2125 | static BOOLEAN kMoraUseBucket(kStrategy strat) |
---|
2126 | { |
---|
2127 | #ifdef MORA_USE_BUCKETS |
---|
2128 | if (TEST_OPT_NOT_BUCKETS) |
---|
2129 | return FALSE; |
---|
2130 | if (strat->red == redFirst) |
---|
2131 | { |
---|
2132 | #ifdef NO_LDEG |
---|
2133 | if (!strat->syzComp) |
---|
2134 | return TRUE; |
---|
2135 | #else |
---|
2136 | if ((strat->homog || strat->honey) && !strat->syzComp) |
---|
2137 | return TRUE; |
---|
2138 | #endif |
---|
2139 | } |
---|
2140 | else |
---|
2141 | { |
---|
2142 | assume(strat->red == redEcart); |
---|
2143 | if (strat->honey && !strat->syzComp) |
---|
2144 | return TRUE; |
---|
2145 | } |
---|
2146 | #endif |
---|
2147 | return FALSE; |
---|
2148 | } |
---|
2149 | */ |
---|
2150 | |
---|
2151 | #ifdef HAVE_ASSUME |
---|
2152 | static int sca_mora_count = 0; |
---|
2153 | static int sca_mora_loop_count; |
---|
2154 | #endif |
---|
2155 | |
---|
2156 | // ideal sca_mora (ideal F, ideal Q, intvec *w, intvec *, kStrategy strat) |
---|
2157 | ideal sca_mora(const ideal F, const ideal Q, const intvec *w, const intvec *, kStrategy strat, const ring _currRing) |
---|
2158 | { |
---|
2159 | /* |
---|
2160 | assume(rIsSCA(currRing)); |
---|
2161 | |
---|
2162 | const unsigned int m_iFirstAltVar = scaFirstAltVar(currRing); |
---|
2163 | const unsigned int m_iLastAltVar = scaLastAltVar(currRing); |
---|
2164 | |
---|
2165 | ideal tempF = id_KillSquares(F, m_iFirstAltVar, m_iLastAltVar, currRing); |
---|
2166 | |
---|
2167 | ideal tempQ = Q; |
---|
2168 | |
---|
2169 | if(Q == currQuotient) |
---|
2170 | tempQ = SCAQuotient(currRing); |
---|
2171 | |
---|
2172 | bool bIdHomog = id_IsSCAHomogeneous(tempF, NULL, NULL, currRing); // wCx == wCy == NULL! |
---|
2173 | |
---|
2174 | assume( !bIdHomog || strat->homog ); // bIdHomog =====[implies]>>>>> strat->homog |
---|
2175 | |
---|
2176 | strat->homog = strat->homog && bIdHomog; |
---|
2177 | |
---|
2178 | #ifdef PDEBUG |
---|
2179 | assume( strat->homog == bIdHomog ); |
---|
2180 | #endif |
---|
2181 | |
---|
2182 | #ifdef HAVE_ASSUME |
---|
2183 | sca_mora_count++; |
---|
2184 | sca_mora_loop_count = 0; |
---|
2185 | #endif |
---|
2186 | |
---|
2187 | #ifdef KDEBUG |
---|
2188 | om_Opts.MinTrack = 5; |
---|
2189 | #endif |
---|
2190 | |
---|
2191 | |
---|
2192 | strat->update = TRUE; |
---|
2193 | //- setting global variables ------------------- - |
---|
2194 | initBuchMoraCrit(strat); |
---|
2195 | // initHilbCrit(F,NULL,&hilb,strat); // no Q! |
---|
2196 | initMora(tempF, strat); |
---|
2197 | initBuchMoraPos(strat); |
---|
2198 | //Shdl= |
---|
2199 | initBuchMora(tempF, tempQ, strat); // temp Q, F! |
---|
2200 | // if (TEST_OPT_FASTHC) missingAxis(&strat->lastAxis,strat); |
---|
2201 | // updateS in initBuchMora has Hecketest |
---|
2202 | // * and could have put strat->kHEdgdeFound FALSE |
---|
2203 | #if 0 |
---|
2204 | if (ppNoether!=NULL) |
---|
2205 | { |
---|
2206 | strat->kHEdgeFound = TRUE; |
---|
2207 | } |
---|
2208 | if (strat->kHEdgeFound && strat->update) |
---|
2209 | { |
---|
2210 | firstUpdate(strat); |
---|
2211 | updateLHC(strat); |
---|
2212 | reorderL(strat); |
---|
2213 | } |
---|
2214 | if (TEST_OPT_FASTHC && (strat->lastAxis) && strat->posInLOldFlag) |
---|
2215 | { |
---|
2216 | strat->posInLOld = strat->posInL; |
---|
2217 | strat->posInLOldFlag = FALSE; |
---|
2218 | strat->posInL = posInL10; |
---|
2219 | updateL(strat); |
---|
2220 | reorderL(strat); |
---|
2221 | } |
---|
2222 | #endif |
---|
2223 | strat->use_buckets = kMoraUseBucket(strat); |
---|
2224 | |
---|
2225 | kTest_TS(strat); |
---|
2226 | |
---|
2227 | |
---|
2228 | int srmax = strat->sl; |
---|
2229 | int lrmax = strat->Ll; |
---|
2230 | int olddeg = 0; |
---|
2231 | int reduc = 0; |
---|
2232 | int red_result = 1; |
---|
2233 | // int hilbeledeg=1; |
---|
2234 | int hilbcount=0; |
---|
2235 | |
---|
2236 | |
---|
2237 | //- compute------------------------------------------- |
---|
2238 | |
---|
2239 | #undef HAVE_TAIL_RING |
---|
2240 | |
---|
2241 | #ifdef HAVE_TAIL_RING |
---|
2242 | // if (strat->homog && strat->red == redFirst) |
---|
2243 | // kStratInitChangeTailRing(strat); |
---|
2244 | #endif |
---|
2245 | |
---|
2246 | |
---|
2247 | |
---|
2248 | |
---|
2249 | |
---|
2250 | // due to std( SB, p) |
---|
2251 | if(TEST_OPT_SB_1) |
---|
2252 | { |
---|
2253 | for (int iNewElement = strat->newIdeal; iNewElement < IDELEMS(tempF); iNewElement++) |
---|
2254 | { |
---|
2255 | |
---|
2256 | const poly pSave = tempF->m[iNewElement]; |
---|
2257 | |
---|
2258 | if( pSave != NULL ) |
---|
2259 | { |
---|
2260 | // tempF->m[iNewElement] = NULL; |
---|
2261 | |
---|
2262 | const poly p_next = pNext(pSave); |
---|
2263 | |
---|
2264 | if(p_next != NULL) |
---|
2265 | for( unsigned int i = m_iFirstAltVar; i <= m_iLastAltVar; i++ ) |
---|
2266 | if( p_GetExp(pSave, i, currRing) != 0 ) |
---|
2267 | { |
---|
2268 | |
---|
2269 | assume(p_GetExp(pSave, i, currRing) == 1); |
---|
2270 | |
---|
2271 | const poly p_new = sca_pp_Mult_xi_pp(i, p_next, currRing); |
---|
2272 | |
---|
2273 | #ifdef PDEBUG |
---|
2274 | p_Test(p_new, currRing); |
---|
2275 | #endif |
---|
2276 | |
---|
2277 | if( p_new == NULL) continue; |
---|
2278 | |
---|
2279 | LObject h(p_new); // h = x_i * strat->P |
---|
2280 | |
---|
2281 | if (TEST_OPT_INTSTRATEGY) |
---|
2282 | h.pCleardenom(); // also does a p_Content |
---|
2283 | else |
---|
2284 | h.pNorm(); |
---|
2285 | |
---|
2286 | strat->initEcart(&h); |
---|
2287 | h.sev = pGetShortExpVector(h.p); |
---|
2288 | |
---|
2289 | int pos = 0; |
---|
2290 | |
---|
2291 | if (strat->Ll != -1) |
---|
2292 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
2293 | |
---|
2294 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
2295 | |
---|
2296 | if (strat->Ll>lrmax) lrmax = strat->Ll; |
---|
2297 | } |
---|
2298 | } |
---|
2299 | |
---|
2300 | } |
---|
2301 | } |
---|
2302 | |
---|
2303 | |
---|
2304 | |
---|
2305 | |
---|
2306 | while (strat->Ll >= 0) |
---|
2307 | { |
---|
2308 | #ifdef HAVE_ASSUME |
---|
2309 | sca_mora_loop_count++; |
---|
2310 | #endif |
---|
2311 | if (lrmax< strat->Ll) lrmax=strat->Ll; // stat |
---|
2312 | //test_int_std(strat->kIdeal); |
---|
2313 | #ifdef KDEBUG |
---|
2314 | if (TEST_OPT_DEBUG) messageSets(strat); |
---|
2315 | #endif |
---|
2316 | if (TEST_OPT_DEGBOUND |
---|
2317 | && (strat->L[strat->Ll].ecart+strat->L[strat->Ll].GetpFDeg()> Kstd1_deg)) |
---|
2318 | { |
---|
2319 | // * stops computation if |
---|
2320 | // * - 24 (degBound) |
---|
2321 | // * && upper degree is bigger than Kstd1_deg |
---|
2322 | while ((strat->Ll >= 0) |
---|
2323 | && (strat->L[strat->Ll].p1!=NULL) && (strat->L[strat->Ll].p2!=NULL) |
---|
2324 | && (strat->L[strat->Ll].ecart+strat->L[strat->Ll].GetpFDeg()> Kstd1_deg) |
---|
2325 | ) |
---|
2326 | { |
---|
2327 | deleteInL(strat->L,&strat->Ll,strat->Ll,strat); |
---|
2328 | //if (TEST_OPT_PROT) |
---|
2329 | //{ |
---|
2330 | // PrintS("D"); mflush(); |
---|
2331 | //} |
---|
2332 | } |
---|
2333 | if (strat->Ll<0) break; |
---|
2334 | else strat->noClearS=TRUE; |
---|
2335 | } |
---|
2336 | strat->P = strat->L[strat->Ll];// - picks the last element from the lazyset L - |
---|
2337 | if (strat->Ll==0) strat->interpt=TRUE; |
---|
2338 | strat->Ll--; |
---|
2339 | |
---|
2340 | // create the real Spoly |
---|
2341 | // assume(pNext(strat->P.p) != strat->tail); |
---|
2342 | |
---|
2343 | if(strat->P.IsNull()) continue; |
---|
2344 | |
---|
2345 | |
---|
2346 | if( pNext(strat->P.p) == strat->tail ) |
---|
2347 | { |
---|
2348 | // deletes the int spoly and computes SPoly |
---|
2349 | pLmFree(strat->P.p); // ??? |
---|
2350 | strat->P.p = nc_CreateSpoly(strat->P.p1, strat->P.p2, currRing); |
---|
2351 | } |
---|
2352 | |
---|
2353 | |
---|
2354 | |
---|
2355 | if (strat->P.p1 == NULL) |
---|
2356 | { |
---|
2357 | // for input polys, prepare reduction (buckets !) |
---|
2358 | strat->P.SetLength(strat->length_pLength); |
---|
2359 | strat->P.PrepareRed(strat->use_buckets); |
---|
2360 | } |
---|
2361 | |
---|
2362 | if (!strat->P.IsNull()) |
---|
2363 | { |
---|
2364 | // might be NULL from noether !!! |
---|
2365 | if (TEST_OPT_PROT) |
---|
2366 | message(strat->P.ecart+strat->P.GetpFDeg(),&olddeg,&reduc,strat, red_result); |
---|
2367 | // reduce |
---|
2368 | red_result = strat->red(&strat->P,strat); |
---|
2369 | } |
---|
2370 | |
---|
2371 | if (! strat->P.IsNull()) |
---|
2372 | { |
---|
2373 | strat->P.GetP(); |
---|
2374 | // statistics |
---|
2375 | if (TEST_OPT_PROT) PrintS("s"); |
---|
2376 | // normalization |
---|
2377 | if (!TEST_OPT_INTSTRATEGY) |
---|
2378 | strat->P.pNorm(); |
---|
2379 | // tailreduction |
---|
2380 | strat->P.p = redtail(&(strat->P),strat->sl,strat); |
---|
2381 | // set ecart -- might have changed because of tail reductions |
---|
2382 | if ((!strat->noTailReduction) && (!strat->honey)) |
---|
2383 | strat->initEcart(&strat->P); |
---|
2384 | // cancel unit |
---|
2385 | cancelunit(&strat->P); |
---|
2386 | // for char 0, clear denominators |
---|
2387 | if (TEST_OPT_INTSTRATEGY) |
---|
2388 | strat->P.pCleardenom(); |
---|
2389 | |
---|
2390 | // put in T |
---|
2391 | enterT(strat->P,strat); |
---|
2392 | // build new pairs |
---|
2393 | enterpairs(strat->P.p,strat->sl,strat->P.ecart,0,strat, strat->tl); |
---|
2394 | // put in S |
---|
2395 | strat->enterS(strat->P, |
---|
2396 | posInS(strat,strat->sl,strat->P.p, strat->P.ecart), |
---|
2397 | strat, strat->tl); |
---|
2398 | |
---|
2399 | |
---|
2400 | // clear strat->P |
---|
2401 | if (strat->P.lcm!=NULL) pLmFree(strat->P.lcm); |
---|
2402 | strat->P.lcm=NULL; |
---|
2403 | |
---|
2404 | if (strat->sl>srmax) srmax = strat->sl; // stat. |
---|
2405 | if (strat->Ll>lrmax) lrmax = strat->Ll; |
---|
2406 | |
---|
2407 | |
---|
2408 | |
---|
2409 | // ////////////////////////////////////////////////////////// |
---|
2410 | // SCA: |
---|
2411 | const poly pSave = strat->P.p; |
---|
2412 | const poly p_next = pNext(pSave); |
---|
2413 | |
---|
2414 | if(p_next != NULL) |
---|
2415 | for( unsigned int i = m_iFirstAltVar; i <= m_iLastAltVar; i++ ) |
---|
2416 | if( p_GetExp(pSave, i, currRing) != 0 ) |
---|
2417 | { |
---|
2418 | |
---|
2419 | assume(p_GetExp(pSave, i, currRing) == 1); |
---|
2420 | |
---|
2421 | const poly p_new = sca_pp_Mult_xi_pp(i, p_next, currRing); |
---|
2422 | |
---|
2423 | #ifdef PDEBUG |
---|
2424 | p_Test(p_new, currRing); |
---|
2425 | #endif |
---|
2426 | |
---|
2427 | if( p_new == NULL) continue; |
---|
2428 | |
---|
2429 | LObject h(p_new); // h = x_i * strat->P |
---|
2430 | |
---|
2431 | if (TEST_OPT_INTSTRATEGY) |
---|
2432 | h.pCleardenom(); // also does a p_Content |
---|
2433 | else |
---|
2434 | h.pNorm(); |
---|
2435 | |
---|
2436 | strat->initEcart(&h); |
---|
2437 | h.sev = pGetShortExpVector(h.p); |
---|
2438 | |
---|
2439 | int pos = 0; |
---|
2440 | |
---|
2441 | if (strat->Ll != -1) |
---|
2442 | pos = strat->posInL(strat->L,strat->Ll,&h,strat); |
---|
2443 | |
---|
2444 | enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos); |
---|
2445 | |
---|
2446 | if (strat->Ll>lrmax) lrmax = strat->Ll; |
---|
2447 | } |
---|
2448 | |
---|
2449 | #ifdef KDEBUG |
---|
2450 | // make sure kTest_TS does not complain about strat->P |
---|
2451 | memset(&strat->P,0,sizeof(strat->P)); |
---|
2452 | #endif |
---|
2453 | } |
---|
2454 | #if 0 |
---|
2455 | if (strat->kHEdgeFound) |
---|
2456 | { |
---|
2457 | if ((TEST_OPT_FINDET) |
---|
2458 | || ((TEST_OPT_MULTBOUND) && (scMult0Int((strat->Shdl)) < mu))) |
---|
2459 | { |
---|
2460 | // obachman: is this still used ??? |
---|
2461 | // * stops computation if strat->kHEdgeFound and |
---|
2462 | // * - 27 (finiteDeterminacyTest) |
---|
2463 | // * or |
---|
2464 | // * - 23 |
---|
2465 | // * (multBound) |
---|
2466 | // * && multiplicity of the ideal is smaller then a predefined number mu |
---|
2467 | while (strat->Ll >= 0) deleteInL(strat->L,&strat->Ll,strat->Ll,strat); |
---|
2468 | } |
---|
2469 | } |
---|
2470 | #endif |
---|
2471 | kTest_TS(strat); |
---|
2472 | } |
---|
2473 | // - complete reduction of the standard basis------------------------ - |
---|
2474 | if (TEST_OPT_REDSB) completeReduce(strat); |
---|
2475 | // - release temp data------------------------------- - |
---|
2476 | exitBuchMora(strat); |
---|
2477 | // - polynomials used for HECKE: HC, noether - |
---|
2478 | if (TEST_OPT_FINDET) |
---|
2479 | { |
---|
2480 | if (strat->kHEdge!=NULL) |
---|
2481 | Kstd1_mu=pFDeg(strat->kHEdge,currRing); |
---|
2482 | else |
---|
2483 | Kstd1_mu=-1; |
---|
2484 | } |
---|
2485 | pDelete(&strat->kHEdge); |
---|
2486 | strat->update = TRUE; //??? |
---|
2487 | strat->lastAxis = 0; //??? |
---|
2488 | pDelete(&strat->kNoether); |
---|
2489 | omFreeSize((ADDRESS)strat->NotUsedAxis,(pVariables+1)*sizeof(BOOLEAN)); |
---|
2490 | if (TEST_OPT_PROT) messageStat(srmax,lrmax,hilbcount,strat); |
---|
2491 | if (TEST_OPT_WEIGHTM) |
---|
2492 | { |
---|
2493 | pRestoreDegProcs(pFDegOld, pLDegOld); |
---|
2494 | if (ecartWeights) |
---|
2495 | { |
---|
2496 | omFreeSize((ADDRESS)ecartWeights,(pVariables+1)*sizeof(short)); |
---|
2497 | ecartWeights=NULL; |
---|
2498 | } |
---|
2499 | } |
---|
2500 | if (tempQ!=NULL) updateResult(strat->Shdl,tempQ,strat); |
---|
2501 | idTest(strat->Shdl); |
---|
2502 | |
---|
2503 | id_Delete( &tempF, currRing); |
---|
2504 | |
---|
2505 | return (strat->Shdl); |
---|
2506 | */ |
---|
2507 | } |
---|
2508 | |
---|
2509 | |
---|
2510 | |
---|
2511 | |
---|
2512 | |
---|
2513 | |
---|
2514 | void sca_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
2515 | { |
---|
2516 | |
---|
2517 | // "commutative" procedures: |
---|
2518 | rGR->p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
2519 | rGR->p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
2520 | |
---|
2521 | p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
2522 | p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
2523 | |
---|
2524 | // non-commutaitve |
---|
2525 | rGR->GetNC()->p_Procs.mm_Mult_p = sca_mm_Mult_p; |
---|
2526 | rGR->GetNC()->p_Procs.mm_Mult_pp = sca_mm_Mult_pp; |
---|
2527 | |
---|
2528 | |
---|
2529 | if (rHasLocalOrMixedOrdering(rGR)) |
---|
2530 | { |
---|
2531 | #ifdef PDEBUG |
---|
2532 | // Print("Local case => GB == mora!\n"); |
---|
2533 | #endif |
---|
2534 | rGR->GetNC()->p_Procs.GB = sca_mora; // local ordering => Mora, otherwise - Buchberger! |
---|
2535 | } |
---|
2536 | else |
---|
2537 | { |
---|
2538 | #ifdef PDEBUG |
---|
2539 | // Print("Global case => GB == bba!\n"); |
---|
2540 | #endif |
---|
2541 | rGR->GetNC()->p_Procs.GB = sca_bba; // sca_gr_bba; // sca_bba? // sca_bba; |
---|
2542 | } |
---|
2543 | |
---|
2544 | |
---|
2545 | // rGR->GetNC()->p_Procs.GlobalGB = sca_gr_bba; |
---|
2546 | // rGR->GetNC()->p_Procs.LocalGB = sca_mora; |
---|
2547 | |
---|
2548 | |
---|
2549 | // rGR->GetNC()->p_Procs.SPoly = sca_SPoly; |
---|
2550 | // rGR->GetNC()->p_Procs.ReduceSPoly = sca_ReduceSpoly; |
---|
2551 | |
---|
2552 | #if 0 |
---|
2553 | |
---|
2554 | // Multiplication procedures: |
---|
2555 | |
---|
2556 | p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
2557 | _p_procs->p_Mult_mm = sca_p_Mult_mm; |
---|
2558 | |
---|
2559 | p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
2560 | _p_procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
2561 | |
---|
2562 | r->GetNC()->mmMultP() = sca_mm_Mult_p; |
---|
2563 | r->GetNC()->mmMultPP() = sca_mm_Mult_pp; |
---|
2564 | |
---|
2565 | r->GetNC()->GB() = sca_gr_bba; |
---|
2566 | /* |
---|
2567 | // ??????????????????????????????????????? coefficients swell... |
---|
2568 | r->GetNC()->SPoly() = sca_SPoly; |
---|
2569 | r->GetNC()->ReduceSPoly() = sca_ReduceSpoly; |
---|
2570 | */ |
---|
2571 | // r->GetNC()->BucketPolyRed() = gnc_kBucketPolyRed; |
---|
2572 | // r->GetNC()->BucketPolyRed_Z()= gnc_kBucketPolyRed_Z; |
---|
2573 | |
---|
2574 | #endif |
---|
2575 | } |
---|
2576 | |
---|
2577 | |
---|
2578 | // bi-Degree (x, y) of monomial "m" |
---|
2579 | // x-es and y-s are weighted by wx and wy resp. |
---|
2580 | // [optional] components have weights by wCx and wCy. |
---|
2581 | static inline void m_GetBiDegree(const poly m, |
---|
2582 | const intvec *wx, const intvec *wy, |
---|
2583 | const intvec *wCx, const intvec *wCy, |
---|
2584 | int& dx, int& dy, const ring r) |
---|
2585 | { |
---|
2586 | const unsigned int N = r->N; |
---|
2587 | |
---|
2588 | p_Test(m, r); |
---|
2589 | |
---|
2590 | assume( wx != NULL ); |
---|
2591 | assume( wy != NULL ); |
---|
2592 | |
---|
2593 | assume( wx->cols() == 1 ); |
---|
2594 | assume( wy->cols() == 1 ); |
---|
2595 | |
---|
2596 | assume( (unsigned int)wx->rows() >= N ); |
---|
2597 | assume( (unsigned int)wy->rows() >= N ); |
---|
2598 | |
---|
2599 | int x = 0; |
---|
2600 | int y = 0; |
---|
2601 | |
---|
2602 | for(int i = N; i > 0; i--) |
---|
2603 | { |
---|
2604 | const int d = p_GetExp(m, i, r); |
---|
2605 | x += d * (*wx)[i-1]; |
---|
2606 | y += d * (*wy)[i-1]; |
---|
2607 | } |
---|
2608 | |
---|
2609 | if( (wCx != NULL) && (wCy != NULL) ) |
---|
2610 | { |
---|
2611 | const int c = p_GetComp(m, r); |
---|
2612 | |
---|
2613 | if( wCx->range(c) ) |
---|
2614 | x += (*wCx)[c]; |
---|
2615 | |
---|
2616 | if( wCy->range(c) ) |
---|
2617 | x += (*wCy)[c]; |
---|
2618 | } |
---|
2619 | |
---|
2620 | dx = x; |
---|
2621 | dy = y; |
---|
2622 | } |
---|
2623 | |
---|
2624 | // returns true if polynom p is bi-homogenous with respect to the given weights |
---|
2625 | // simultaneously sets bi-Degree |
---|
2626 | bool p_IsBiHomogeneous(const poly p, |
---|
2627 | const intvec *wx, const intvec *wy, |
---|
2628 | const intvec *wCx, const intvec *wCy, |
---|
2629 | int &dx, int &dy, |
---|
2630 | const ring r) |
---|
2631 | { |
---|
2632 | if( p == NULL ) |
---|
2633 | { |
---|
2634 | dx = 0; |
---|
2635 | dy = 0; |
---|
2636 | return true; |
---|
2637 | } |
---|
2638 | |
---|
2639 | poly q = p; |
---|
2640 | |
---|
2641 | |
---|
2642 | int ddx, ddy; |
---|
2643 | |
---|
2644 | m_GetBiDegree( q, wx, wy, wCx, wCy, ddx, ddy, r); // get bi degree of lm(p) |
---|
2645 | |
---|
2646 | pIter(q); |
---|
2647 | |
---|
2648 | for(; q != NULL; pIter(q) ) |
---|
2649 | { |
---|
2650 | int x, y; |
---|
2651 | |
---|
2652 | m_GetBiDegree( q, wx, wy, wCx, wCy, x, y, r); // get bi degree of q |
---|
2653 | |
---|
2654 | if ( (x != ddx) || (y != ddy) ) return false; |
---|
2655 | } |
---|
2656 | |
---|
2657 | dx = ddx; |
---|
2658 | dy = ddy; |
---|
2659 | |
---|
2660 | return true; |
---|
2661 | } |
---|
2662 | |
---|
2663 | |
---|
2664 | // returns true if id is bi-homogenous without respect to the given weights |
---|
2665 | bool id_IsBiHomogeneous(const ideal id, |
---|
2666 | const intvec *wx, const intvec *wy, |
---|
2667 | const intvec *wCx, const intvec *wCy, |
---|
2668 | const ring r) |
---|
2669 | { |
---|
2670 | if (id == NULL) return true; // zero ideal |
---|
2671 | |
---|
2672 | const int iSize = IDELEMS(id); |
---|
2673 | |
---|
2674 | if (iSize == 0) return true; |
---|
2675 | |
---|
2676 | bool b = true; |
---|
2677 | int x, y; |
---|
2678 | |
---|
2679 | for(int i = iSize - 1; (i >= 0 ) && b; i--) |
---|
2680 | b = p_IsBiHomogeneous(id->m[i], wx, wy, wCx, wCy, x, y, r); |
---|
2681 | |
---|
2682 | return b; |
---|
2683 | } |
---|
2684 | |
---|
2685 | |
---|
2686 | // returns an intvector with [nvars(r)] integers [1/0] |
---|
2687 | // 1 - for commutative variables |
---|
2688 | // 0 - for anticommutative variables |
---|
2689 | intvec *ivGetSCAXVarWeights(const ring r) |
---|
2690 | { |
---|
2691 | const unsigned int N = r->N; |
---|
2692 | |
---|
2693 | const int CommutativeVariable = 0; // bug correction! |
---|
2694 | const int AntiCommutativeVariable = 0; |
---|
2695 | |
---|
2696 | intvec* w = new intvec(N, 1, CommutativeVariable); |
---|
2697 | |
---|
2698 | if(AntiCommutativeVariable != CommutativeVariable) |
---|
2699 | if( rIsSCA(r) ) |
---|
2700 | { |
---|
2701 | const unsigned int m_iFirstAltVar = scaFirstAltVar(r); |
---|
2702 | const unsigned int m_iLastAltVar = scaLastAltVar(r); |
---|
2703 | |
---|
2704 | for (unsigned int i = m_iFirstAltVar; i<= m_iLastAltVar; i++) |
---|
2705 | { |
---|
2706 | (*w)[i-1] = AntiCommutativeVariable; |
---|
2707 | } |
---|
2708 | } |
---|
2709 | |
---|
2710 | return w; |
---|
2711 | } |
---|
2712 | |
---|
2713 | |
---|
2714 | // returns an intvector with [nvars(r)] integers [1/0] |
---|
2715 | // 0 - for commutative variables |
---|
2716 | // 1 - for anticommutative variables |
---|
2717 | intvec *ivGetSCAYVarWeights(const ring r) |
---|
2718 | { |
---|
2719 | const unsigned int N = r->N; |
---|
2720 | |
---|
2721 | const int CommutativeVariable = 0; |
---|
2722 | const int AntiCommutativeVariable = 1; |
---|
2723 | |
---|
2724 | intvec* w = new intvec(N, 1, CommutativeVariable); |
---|
2725 | |
---|
2726 | if(AntiCommutativeVariable != CommutativeVariable) |
---|
2727 | if( rIsSCA(r) ) |
---|
2728 | { |
---|
2729 | const unsigned int m_iFirstAltVar = scaFirstAltVar(r); |
---|
2730 | const unsigned int m_iLastAltVar = scaLastAltVar(r); |
---|
2731 | |
---|
2732 | for (unsigned int i = m_iFirstAltVar; i<= m_iLastAltVar; i++) |
---|
2733 | { |
---|
2734 | (*w)[i-1] = AntiCommutativeVariable; |
---|
2735 | } |
---|
2736 | } |
---|
2737 | return w; |
---|
2738 | } |
---|
2739 | |
---|
2740 | |
---|
2741 | |
---|
2742 | |
---|
2743 | // reduce term lt(m) modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar: |
---|
2744 | // either create a copy of m or return NULL |
---|
2745 | static inline poly m_KillSquares(const poly m, |
---|
2746 | const unsigned int iFirstAltVar, const unsigned int iLastAltVar, |
---|
2747 | const ring r) |
---|
2748 | { |
---|
2749 | #ifdef PDEBUG |
---|
2750 | p_Test(m, r); |
---|
2751 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= r->N) && (iFirstAltVar <= iLastAltVar) ); |
---|
2752 | |
---|
2753 | #if 0 |
---|
2754 | Print("m_KillSquares, m = "); // ! |
---|
2755 | p_Write(m, r); |
---|
2756 | #endif |
---|
2757 | #endif |
---|
2758 | |
---|
2759 | assume( m != NULL ); |
---|
2760 | |
---|
2761 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
2762 | if( p_GetExp(m, k, r) > 1 ) |
---|
2763 | return NULL; |
---|
2764 | |
---|
2765 | return p_Head(m, r); |
---|
2766 | } |
---|
2767 | |
---|
2768 | |
---|
2769 | // reduce polynomial p modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar |
---|
2770 | // returns a new poly! |
---|
2771 | poly p_KillSquares(const poly p, |
---|
2772 | const unsigned int iFirstAltVar, const unsigned int iLastAltVar, |
---|
2773 | const ring r) |
---|
2774 | { |
---|
2775 | #ifdef PDEBUG |
---|
2776 | p_Test(p, r); |
---|
2777 | |
---|
2778 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= r->N) && (iFirstAltVar <= iLastAltVar) ); |
---|
2779 | |
---|
2780 | #if 0 |
---|
2781 | Print("p_KillSquares, p = "); // ! |
---|
2782 | p_Write(p, r); |
---|
2783 | #endif |
---|
2784 | #endif |
---|
2785 | |
---|
2786 | |
---|
2787 | if( p == NULL ) |
---|
2788 | return NULL; |
---|
2789 | |
---|
2790 | poly pResult = NULL; |
---|
2791 | poly* ppPrev = &pResult; |
---|
2792 | |
---|
2793 | for( poly q = p; q!= NULL; pIter(q) ) |
---|
2794 | { |
---|
2795 | #ifdef PDEBUG |
---|
2796 | p_Test(q, r); |
---|
2797 | #endif |
---|
2798 | |
---|
2799 | // terms will be in the same order because of quasi-ordering! |
---|
2800 | poly v = m_KillSquares(q, iFirstAltVar, iLastAltVar, r); |
---|
2801 | |
---|
2802 | if( v != NULL ) |
---|
2803 | { |
---|
2804 | *ppPrev = v; |
---|
2805 | ppPrev = &pNext(v); |
---|
2806 | } |
---|
2807 | |
---|
2808 | } |
---|
2809 | |
---|
2810 | #ifdef PDEBUG |
---|
2811 | p_Test(pResult, r); |
---|
2812 | #if 0 |
---|
2813 | Print("p_KillSquares => "); // ! |
---|
2814 | p_Write(pResult, r); |
---|
2815 | #endif |
---|
2816 | #endif |
---|
2817 | |
---|
2818 | return(pResult); |
---|
2819 | } |
---|
2820 | |
---|
2821 | |
---|
2822 | |
---|
2823 | |
---|
2824 | // reduces ideal id modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar |
---|
2825 | // returns the reduced ideal or zero ideal. |
---|
2826 | ideal id_KillSquares(const ideal id, |
---|
2827 | const unsigned int iFirstAltVar, const unsigned int iLastAltVar, |
---|
2828 | const ring r, const bool bSkipZeroes) |
---|
2829 | { |
---|
2830 | if (id == NULL) return id; // zero ideal |
---|
2831 | |
---|
2832 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= r->N) && (iFirstAltVar <= iLastAltVar) ); |
---|
2833 | |
---|
2834 | const int iSize = IDELEMS(id); |
---|
2835 | |
---|
2836 | if (iSize == 0) return id; |
---|
2837 | |
---|
2838 | ideal temp = idInit(iSize, id->rank); |
---|
2839 | |
---|
2840 | #if 0 |
---|
2841 | PrintS("<id_KillSquares>\n"); |
---|
2842 | { |
---|
2843 | PrintS("ideal id: \n"); |
---|
2844 | for (int i = 0; i < IDELEMS(id); i++) |
---|
2845 | { |
---|
2846 | Print("; id[%d] = ", i+1); |
---|
2847 | p_Write(id->m[i], r); |
---|
2848 | } |
---|
2849 | PrintS(";\n"); |
---|
2850 | PrintLn(); |
---|
2851 | } |
---|
2852 | #endif |
---|
2853 | |
---|
2854 | |
---|
2855 | for (int j = 0; j < iSize; j++) |
---|
2856 | temp->m[j] = p_KillSquares(id->m[j], iFirstAltVar, iLastAltVar, r); |
---|
2857 | |
---|
2858 | if( bSkipZeroes ) |
---|
2859 | idSkipZeroes(temp); |
---|
2860 | |
---|
2861 | #if 0 |
---|
2862 | PrintS("<id_KillSquares>\n"); |
---|
2863 | { |
---|
2864 | PrintS("ideal temp: \n"); |
---|
2865 | for (int i = 0; i < IDELEMS(temp); i++) |
---|
2866 | { |
---|
2867 | Print("; temp[%d] = ", i+1); |
---|
2868 | p_Write(temp->m[i], r); |
---|
2869 | } |
---|
2870 | PrintS(";\n"); |
---|
2871 | PrintLn(); |
---|
2872 | } |
---|
2873 | PrintS("</id_KillSquares>\n"); |
---|
2874 | #endif |
---|
2875 | |
---|
2876 | // temp->rank = idRankFreeModule(temp, r); |
---|
2877 | |
---|
2878 | return temp; |
---|
2879 | } |
---|
2880 | |
---|
2881 | |
---|
2882 | |
---|
2883 | |
---|
2884 | #endif |
---|